Podcast
Questions and Answers
A surveyor needs to determine the height of a building. Standing some distance away, they measure the angle of elevation to the top of the building. What additional piece of information is required to calculate the building's height using trigonometric ratios?
A surveyor needs to determine the height of a building. Standing some distance away, they measure the angle of elevation to the top of the building. What additional piece of information is required to calculate the building's height using trigonometric ratios?
- The surveyor's height.
- The angle of depression from the top of the building.
- The distance from the surveyor to the base of the building. (correct)
- The material the building is made of.
In a triangle, two angles measure 45° and 75° respectively. If the side opposite the 45° angle is 10 cm, what is the approximate length of the side opposite the 75° angle?
In a triangle, two angles measure 45° and 75° respectively. If the side opposite the 45° angle is 10 cm, what is the approximate length of the side opposite the 75° angle?
- 14.14 cm
- 8.16 cm
- 10.25 cm
- 12.25 cm (correct)
A gardener needs to fence a triangular plot of land. Two sides of the plot measure 15 meters and 20 meters, and the angle between them is 60°. What is the approximate length of fencing required for the third side?
A gardener needs to fence a triangular plot of land. Two sides of the plot measure 15 meters and 20 meters, and the angle between them is 60°. What is the approximate length of fencing required for the third side?
- 17 meters
- 25 meters
- 18 meters (correct)
- 21 meters
Two triangles are similar. The sides of the smaller triangle are 3 cm, 5 cm, and 6 cm. If the longest side of the larger triangle is 18 cm, what is the perimeter of the larger triangle?
Two triangles are similar. The sides of the smaller triangle are 3 cm, 5 cm, and 6 cm. If the longest side of the larger triangle is 18 cm, what is the perimeter of the larger triangle?
In a non-right-angled triangle, you know the lengths of all three sides. Which rule should you use to find the measure of one of the angles?
In a non-right-angled triangle, you know the lengths of all three sides. Which rule should you use to find the measure of one of the angles?
A ladder leans against a wall, forming a right-angled triangle. The ladder is 6 meters long, and its base is 2 meters away from the wall. What trigonometric ratio can be used to find the angle between the ladder and the ground?
A ladder leans against a wall, forming a right-angled triangle. The ladder is 6 meters long, and its base is 2 meters away from the wall. What trigonometric ratio can be used to find the angle between the ladder and the ground?
In triangle ABC, angle A is 30°, side b is 12 cm, and side a is 8 cm. How many possible values are there for angle B?
In triangle ABC, angle A is 30°, side b is 12 cm, and side a is 8 cm. How many possible values are there for angle B?
You are given two triangles. Triangle PQR has angles 60°, 80°, and 40°. Triangle XYZ has angles 80°, 40°, and 60°. Side PQ is 5cm. What additional piece of information is needed to prove that the two triangles are congruent?
You are given two triangles. Triangle PQR has angles 60°, 80°, and 40°. Triangle XYZ has angles 80°, 40°, and 60°. Side PQ is 5cm. What additional piece of information is needed to prove that the two triangles are congruent?
A building casts a shadow of 30 meters when a 5-meter pole casts a shadow of 3 meters. Assuming the angles of elevation are the same, how tall is the building?
A building casts a shadow of 30 meters when a 5-meter pole casts a shadow of 3 meters. Assuming the angles of elevation are the same, how tall is the building?
In a triangle ABC, angle A is 50 degrees, side b is 15 cm, and side c is 12 cm. Which rule would you use to find the length of side a?
In a triangle ABC, angle A is 50 degrees, side b is 15 cm, and side c is 12 cm. Which rule would you use to find the length of side a?
You need to find the height of a cliff. You stand some distance away from the base and measure the angle of elevation to the top. From a closer point, the angle of elevation is larger. What principle prevents you from directly calculating the height with only one angle measurement?
You need to find the height of a cliff. You stand some distance away from the base and measure the angle of elevation to the top. From a closer point, the angle of elevation is larger. What principle prevents you from directly calculating the height with only one angle measurement?
Triangle PQR has sides p = 5 cm, q = 7 cm, and r = 8 cm. Which angle is the largest in the triangle?
Triangle PQR has sides p = 5 cm, q = 7 cm, and r = 8 cm. Which angle is the largest in the triangle?
In a triangle XYZ, XY = 10 cm, YZ = 8 cm and angle XYZ = 30°. Find the area of the triangle.
In a triangle XYZ, XY = 10 cm, YZ = 8 cm and angle XYZ = 30°. Find the area of the triangle.
Two buildings are 50 meters apart. From the top of the shorter building, the angle of elevation to the top of the taller building is 15 degrees, and the angle of depression to the base of the taller building is 30 degrees. Approximately, what is the height difference between the two buildings?
Two buildings are 50 meters apart. From the top of the shorter building, the angle of elevation to the top of the taller building is 15 degrees, and the angle of depression to the base of the taller building is 30 degrees. Approximately, what is the height difference between the two buildings?
Two similar triangles have areas of 36 $cm^2$ and 81 $cm^2$. If the perimeter of the smaller triangle is 30 cm, what is the perimeter of the larger triangle?
Two similar triangles have areas of 36 $cm^2$ and 81 $cm^2$. If the perimeter of the smaller triangle is 30 cm, what is the perimeter of the larger triangle?
Flashcards
SOHCAHTOA
SOHCAHTOA
Trigonometric ratios for right-angled triangles: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
Sine Rule
Sine Rule
A rule used to find missing sides or angles in non-right-angled triangles, relating sides to the sines of their opposite angles.
Cosine Rule
Cosine Rule
A rule used to find missing sides or angles in non-right-angled triangles, involving the squares of the sides and the cosine of an angle.
Similar Triangles
Similar Triangles
Signup and view all the flashcards
Finding Angles
Finding Angles
Signup and view all the flashcards
Angle Sum Rule
Angle Sum Rule
Signup and view all the flashcards
When to Use SOHCAHTOA
When to Use SOHCAHTOA
Signup and view all the flashcards
When to Use the Sine Rule
When to Use the Sine Rule
Signup and view all the flashcards
When to Use the Cosine Rule
When to Use the Cosine Rule
Signup and view all the flashcards
Study Notes
- This podcast episode is a mathematics masterclass for MYP5 students
- It covers trigonometric ratios, sine and cosine rules, similar triangles, and finding missing angles in non-right-angled triangles
- The episode aims to help students prepare for upcoming math assessments in about 20 minutes
Trigonometric Ratios (SOHCAHTOA)
- SOHCAHTOA applies to right-angled triangles
- Sine is opposite divided by hypotenuse
- Cosine is adjacent divided by hypotenuse
- Tangent is opposite divided by adjacent
- If a ramp makes a 35° angle with the ground and is 5m long, its height can be found using sine: sin(35°) = x/5, so x ≈ 2.87m
- SOHCAHTOA is useful for finding a missing side or angle
Sine Rule
- The Sine Rule applies to non-right-angled triangles
- The formula is a/sin(A) = b/sin(B) = c/sin(C)
- Use it when you know two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA)
- E.g to find angle B where a=8cm, b=10cm, and A=40°, use 8/sin(40°) = 10/sin(B), so B ≈ 53.1°
- Sine Rule is useful when you have opposite pairs of angles and sides
Cosine Rule
- Cosine Rule applies to non-right-angled triangles when you don't have an opposite pair
- The formula is c² = a² + b² - 2ab cos(C)
- Use it when you know two sides and the included angle (SAS) or all three sides (SSS) and need an angle
- E.g to find angle C where a=7cm, b=9cm, and c=10cm, use cos(C) = (7² + 9² - 10²)/(279), so C ≈ 76.2°
- Cosine Rule should be used when Sine Rule won't work
Similar Triangles
- Triangles are similar if their angles are equal and their sides are in proportion
- To find the height of a tower, if a 2-meter stick casts a 1.5-meter shadow, while a tower casts a 15-meter shadow (2/1.5 = x/15), then the height of the tower is 20 meters
- Use similar triangles in real-world scaling problems
Finding Angles in Non-Right-Angled Triangles
- To find missing angles, three methods are available
- The Sine Rule is used if you have an opposite pair
- The Cosine Rule is used if you know all three sides (SSS)
- The Angle Sum Rule is used if you already know two angles, using A + B + C = 180°
- E.g to find C if A = 65° and B = 75°, then C = 180° - (65° + 75°) = 40°
Recap & Final Tips
- Concepts outlined includes Pythagoras’ Theorem, SOHCAHTOA, Sine & Cosine Rule, Similar Triangles, and Finding Missing Angles
- It's important to practice these concepts and apply them to past exam questions
- Always check whether your triangle is right-angled or not before deciding which formula to use
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
