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Questions and Answers
State the 6 basic trigonometric functions and their ratios.
Sine (sin), Cosine (cos), Tangent (tan), Cosecant (csc), Secant (sec), Cotangent (cot).
Given a right triangle with an angle of 30 degrees and an adjacent side of length 3. Find the length of the hypotenuse.
$$6$$
A tower casts a 50-foot long shadow on the ground. If the angle of elevation from the tip of the shadow to the top of the tower is 60 degrees, find the height of the tower.
$$25\sqrt{3}$$ feet
Calculate the area of a triangle with sides of length 5, 7, and 8.
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In a right triangle, if the side opposite an angle is 12 and the hypotenuse is 15, find the measure of the angle.
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Find the value of $x$ in the right triangle below, given that $ an(x) = \frac{3}{4}$:
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A ladder is leaning against a wall. If the ladder makes an angle of 70 degrees with the ground and the foot of the ladder is 7 meters away from the wall, find the length of the ladder.
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In a non-right triangle $ABC$, if side $a=8$, side $b=10$, and angle $C=30$ degrees, find the area of the triangle.
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A person standing on top of a building sees a car at a 40-degree angle of depression. If the building is 100 feet tall, find the horizontal distance from the person to the car.
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In a triangle $XYZ$, if side $x=12$, side $y=15$, and angle $Z=45$ degrees, find the length of side $z$.
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Study Notes
Trigonometric Functions
- The 6 basic trig functions and their ratios are:
- Sine (sin): opposite side / hypotenuse
- Cosine (cos): adjacent side / hypotenuse
- Tangent (tan): opposite side / adjacent side
- Cotangent (cot): adjacent side / opposite side
- Secant (sec): hypotenuse / adjacent side
- Cosecant (csc): hypotenuse / opposite side
Solving Right Triangles
- Given a right triangle with known sides and/or angles, use trig functions to find missing sides and angles
- Example: In a right triangle, the length of the hypotenuse is 10 units and one of the acute angles is 30°. Find the length of the opposite side.
Angles of Elevation and Depression
- Angle of elevation: the angle between the line of sight and the horizontal when the object is above the observer
- Angle of depression: the angle between the line of sight and the horizontal when the object is below the observer
- Example: A observer looks up at a building and measures an angle of elevation of 60°. If the distance to the building is 50 meters, how tall is the building?
Non-Right Triangle Area
- The area of a non-right triangle can be found using trigonometric functions
- Example: Find the area of a triangle with sides of length 5, 7, and 9 units.
Unsolved Questions
- In a right triangle, the length of the hypotenuse is 12 units and one of the acute angles is 45°. Find the length of the adjacent side.
- A surveyor measures an angle of depression of 35° to a point on the ground. If the distance to the point is 25 meters, how high is the surveyor above the ground?
- Find the area of a triangle with sides of length 3, 4, and 5 units.
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Description
Test your knowledge on the 6 basic trigonometric functions and their ratios, solving for missing sides and angles in right triangles using trigonometry. Includes word problems on angles of elevation and depression, as well as questions on finding the area of non-right triangles. Some questions may not have a solution.
