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10th grade trigonometry

10th grade (Year 11 in England) · 16 questions · Common Core: HSG.SRT.C.6, HSG.SRT.C.8, HSF.TF.A.3 · England: GCSE Foundation Geometry, GCSE Higher Geometry

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1
Question 1
In a right triangle you know angle θ and the opposite side. You want the hypotenuse. Which ratio should you use?
- A. sin
- B. cos
- C. tan
2
Question 2
A 13 m ladder leans against a wall at 47° to the ground. To find how high up the wall it reaches, which ratio do you use with the 47° angle?
- A. sin
- B. cos
- C. tan
3
Question 3
In triangle YNZ, the right angle is at N. Using angle Y, which side is the adjacent?
- A. YN
- B. YZ
- C. NZ
4
Question 4
What is the exact value of sin 90°?
- A. 1
- B. 0
- C. √3/2
- D. √3/3
Question 5
A right triangle has hypotenuse 12 cm and a 30° angle. Find the side opposite the 30° angle. Give an exact answer.
Answer
Question 6
A ramp rises at 44° over a horizontal distance of 9 m. How high does it rise? Give 1 decimal place.
Answer
Question 7
Maya stands 44 m from the base of a tower. The angle of elevation to the top is 20°. How tall is the tower, to the nearest metre? (Ignore Maya's height.)
Answer
Question 8
An equilateral triangle has sides of 18 cm. Find its exact height.
Answer
Question 9
A right triangle has opposite side 13 cm and adjacent side 6 cm to angle θ. Find θ to 1 decimal place.
Answer
Question 10
Jamal flies a drone 14 m above the ground. From where Jamal stands, the angle of elevation to the drone is 38°. How far horizontally is the drone from Jamal? Give 1 decimal place.
Answer
11
Question 11
In the right triangle, which side is the hypotenuse?
- A. t
- B. s
- C. q
12
Question 12
In a right triangle, angle θ has opposite side 3, adjacent side 4 and hypotenuse 5. What is tan θ?
- A. 3/5
- B. 3/4
- C. 4/3
- D. 4/5
Question 13
In a right triangle the hypotenuse is 26 m and the side opposite angle θ is 12 m. Find θ to 1 decimal place.
Answer
Question 14
In a right triangle, the side adjacent to a 39° angle is 20 cm. Find the hypotenuse to 1 decimal place.
Answer
Question 15
A right triangle has hypotenuse 27 cm and an angle of 48°. Find the side opposite the 48° angle, to 1 decimal place.
Answer
Question 16
From the top of a 28 m cliff, the angle of depression to a boat is 29°. How far is the boat from the foot of the cliff? Round to the nearest metre.
Answer

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