Trigonometry Problems and Ratios

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If $\sin(35^\circ) = \frac{30}{x}$, what is the value of x rounded to the nearest tenth?

25.6

52.3

52.9 (correct)

17.2

If $\cos(27^\circ)=\frac{16}{x}$, then x is approximately 17.9.

True

If $\tan(70^\circ) = \frac{x}{18}$, what is x rounded to the nearest tenth?

49.5

If $\sin(58^\circ) = \frac{29}{x}$, then x is approximately ______ when rounded to the nearest tenth.

34.1 Signup and view all the answers

Match the trigonometric function with its corresponding ratio, given angle $\theta$ and sides opposite, adjacent and hypotenuse from said angle:

$\sin(\theta)$ = opposite/hypotenuse $\cos(\theta)$ = adjacent/hypotenuse $\tan(\theta)$ = opposite/adjacent Signup and view all the answers

A right triangle has an adjacent side of 4 and an opposite side of 14. What is the measure of the angle opposite the side of length 4 (to the nearest degree)?

74° Signup and view all the answers

Given: a right triangle with an adjacent side of 29 and the hypotenuse of 59. The angle adjacent to the side of length 29 is approximately 29.94 degrees.

False Signup and view all the answers

In a right triangle, if the adjacent side is 7 and the hypotenuse is 9, what is the approximate measure of the angle adjacent to the side of length 7 (to the nearest degree)?

39 Signup and view all the answers

If the opposite side of a right triangle is 35 and the adjacent side is 8, the angle opposite the side of length 35, rounded to the nearest degree, is ______.

77 Signup and view all the answers

Match the trigonometric ratio with the correct calculation:

$sin(x)$ = Opposite / Hypotenuse $cos(x)$ = Adjacent / Hypotenuse $tan(x)$ = Opposite / Adjacent Signup and view all the answers

What is the approximate length of the side adjacent to the 73-degree angle in a right triangle, if the opposite side is 18 units long?

5.9 Signup and view all the answers

In a right triangle with a 60-degree angle and an opposite side of length 11, the adjacent side is approximately 9.8.

False Signup and view all the answers

A right triangle has a 22-degree angle and one side of 12 units opposite this angle. What is the approximate length of the adjacent side?

7.7 Signup and view all the answers

In a right triangle, if the angle is 17 degrees and the side opposite this angle is 16, the adjacent side is approximately ______.

57.3 Signup and view all the answers

Match the angle and side length with the approximate length of the adjacent side using the tangent function:

23 degrees, opposite side 20 = 8.5 39 degrees, opposite side 10 = 12.8 61 degrees, opposite side 14 = 7.8 44 degrees, opposite side 17 = 17.3 Signup and view all the answers

In a right triangle with an angle of $59^{\circ}$ and an adjacent side of 11, what is the length of the opposite side, rounded to the nearest tenth?

18.3 Signup and view all the answers

If a triangle has a $21^{\circ}$ angle, and the side opposite to that angle is 19, the adjacent side of the triangle will be approximately 49.6.

True Signup and view all the answers

In a right triangle with a $67^{\circ}$ angle, the length of the side opposite to the angle is 19. What is the approximate length of the side adjacent to that angle, rounded to the nearest tenth?

8.0 Signup and view all the answers

In a right triangle, with a $43^{\circ}$ angle, if the side adjacent to the angle measures $19$, then the length of the opposite side of the triangle is approximately ____.

17.7 Signup and view all the answers

Match the given triangle angle and side information to the appropriate calculation for the length, x:

Angle $46^{\circ}$, opposite side x, adjacent side 16 = $x = 16 \times \text{tan }46^{\circ}$ Angle $67^{\circ}$, opposite side 19, adjacent side x = $x = \frac{19}{\text{tan }67^{\circ}}$ Angle $52^{\circ}$, opposite side 17, adjacent side x = $x = \frac{17}{\text{tan }52^{\circ}}$ Angle $24^{\circ}$, opposite side 24, adjacent side x = This information is not sufficient to calculate x. Signup and view all the answers

In a right triangle, if the angle is 27 degrees and the opposite side is 5, what is the length of the adjacent side, rounded to the nearest tenth?

9.8 Signup and view all the answers

Given a right triangle with a 62-degree angle and an adjacent side of 38, the hypotenuse is approximately 50.5 when rounded to the nearest tenth.

False Signup and view all the answers

In a right triangle with a 39-degree angle and an adjacent side of 40, what is the length of the opposite side, rounded to the nearest tenth?

32.4 Signup and view all the answers

In a right triangle with a 18-degree angle and a hypotenuse of 48, the length of the opposite side can be calculated using the _______ function.

sine Signup and view all the answers

Match the trigonometric functions with their correct ratios in a right triangle

Sine = Opposite / Hypotenuse Cosine = Adjacent / Hypotenuse Tangent = Opposite / Adjacent Signup and view all the answers

A 30 ft ladder leans against a building, forming a 70° angle with the ground. Approximately how far is the base of the ladder from the building?

28.2 ft Signup and view all the answers

If a tree casts a 32 foot shadow and the angle of elevation of the sun is 58°, then the height of the tree is approximately 30 feet.

False Signup and view all the answers

A kite is flying with 100 ft of string at an angle of 80°. If the spool is 5 ft above the ground, approximately how high is the kite above the ground?

103.5 ft Signup and view all the answers

From the top of a 230 ft lighthouse, the angle of depression to the boat at sea is 42°. The approximate distance from the boat to the foot of the lighthouse is ______ ft.

255.4 Signup and view all the answers

Simon wants a sign for his building. The angle of elevation to the roof is 31°, and to the top of the sign is 42°. Point P is 24 ft from the building. Approximately how tall is the sign?

6.9 ft Signup and view all the answers

A tree leaning at a 24° angle against a building, with a length of 20 ft, results in a building height of approximately 20 ft.

False Signup and view all the answers

Match the scenarios to the trigonometric functions used for their solution:

Ladder against building (base distance) = sine Tree height from its shadow = tangent Kite height above the ground = sine Distance from boat to the lighthouse foot = tangent Signup and view all the answers

If a tree casts a 32-foot shadow and the angle of elevation of the sun is 58°, provide the formula for finding the height of the tree. (Use trigonometric function and variable x to represent the tree height).

<code>tan(58°) = x / 32</code> Signup and view all the answers

Trigonometry Problems and Ratios

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Questions and Answers

If $\sin(35^\circ) = \frac{30}{x}$, what is the value of x rounded to the nearest tenth?

If $\cos(27^\circ)=\frac{16}{x}$, then x is approximately 17.9.

If $\tan(70^\circ) = \frac{x}{18}$, what is x rounded to the nearest tenth?

If $\sin(58^\circ) = \frac{29}{x}$, then x is approximately ______ when rounded to the nearest tenth.

Match the trigonometric function with its corresponding ratio, given angle $\theta$ and sides opposite, adjacent and hypotenuse from said angle:

A right triangle has an adjacent side of 4 and an opposite side of 14. What is the measure of the angle opposite the side of length 4 (to the nearest degree)?

Given: a right triangle with an adjacent side of 29 and the hypotenuse of 59. The angle adjacent to the side of length 29 is approximately 29.94 degrees.

In a right triangle, if the adjacent side is 7 and the hypotenuse is 9, what is the approximate measure of the angle adjacent to the side of length 7 (to the nearest degree)?

If the opposite side of a right triangle is 35 and the adjacent side is 8, the angle opposite the side of length 35, rounded to the nearest degree, is ______.

Match the trigonometric ratio with the correct calculation:

What is the approximate length of the side adjacent to the 73-degree angle in a right triangle, if the opposite side is 18 units long?

In a right triangle with a 60-degree angle and an opposite side of length 11, the adjacent side is approximately 9.8.

A right triangle has a 22-degree angle and one side of 12 units opposite this angle. What is the approximate length of the adjacent side?

In a right triangle, if the angle is 17 degrees and the side opposite this angle is 16, the adjacent side is approximately ______.

Match the angle and side length with the approximate length of the adjacent side using the tangent function:

In a right triangle with an angle of $59^{\circ}$ and an adjacent side of 11, what is the length of the opposite side, rounded to the nearest tenth?

If a triangle has a $21^{\circ}$ angle, and the side opposite to that angle is 19, the adjacent side of the triangle will be approximately 49.6.

In a right triangle with a $67^{\circ}$ angle, the length of the side opposite to the angle is 19. What is the approximate length of the side adjacent to that angle, rounded to the nearest tenth?

In a right triangle, with a $43^{\circ}$ angle, if the side adjacent to the angle measures $19$, then the length of the opposite side of the triangle is approximately ____.

Match the given triangle angle and side information to the appropriate calculation for the length, x:

In a right triangle, if the angle is 27 degrees and the opposite side is 5, what is the length of the adjacent side, rounded to the nearest tenth?

Given a right triangle with a 62-degree angle and an adjacent side of 38, the hypotenuse is approximately 50.5 when rounded to the nearest tenth.

In a right triangle with a 39-degree angle and an adjacent side of 40, what is the length of the opposite side, rounded to the nearest tenth?

In a right triangle with a 18-degree angle and a hypotenuse of 48, the length of the opposite side can be calculated using the _______ function.

Match the trigonometric functions with their correct ratios in a right triangle

A 30 ft ladder leans against a building, forming a 70° angle with the ground. Approximately how far is the base of the ladder from the building?

If a tree casts a 32 foot shadow and the angle of elevation of the sun is 58°, then the height of the tree is approximately 30 feet.

A kite is flying with 100 ft of string at an angle of 80°. If the spool is 5 ft above the ground, approximately how high is the kite above the ground?

From the top of a 230 ft lighthouse, the angle of depression to the boat at sea is 42°. The approximate distance from the boat to the foot of the lighthouse is ______ ft.

Simon wants a sign for his building. The angle of elevation to the roof is 31°, and to the top of the sign is 42°. Point P is 24 ft from the building. Approximately how tall is the sign?

A tree leaning at a 24° angle against a building, with a length of 20 ft, results in a building height of approximately 20 ft.

Match the scenarios to the trigonometric functions used for their solution:

If a tree casts a 32-foot shadow and the angle of elevation of the sun is 58°, provide the formula for finding the height of the tree. (Use trigonometric function and variable x to represent the tree height).

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