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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Date
Score/ 16
Question 1
From the top of a 100 m cliff, the angle of depression to a boat is 54°. How far is the boat from the foot of the cliff? Round to the nearest metre.
Answer
Question 2
In a right triangle you know angle θ and the adjacent side. You want the opposite side. Which ratio should you use?
- A. sin
- B. cos
- C. tan
Question 3
In triangle QZX, the right angle is at Z. Using angle Q, which side is the adjacent?
- A. QX
- B. ZX
- C. QZ
Question 4
A right triangle has opposite side 10 cm and adjacent side 6 cm to angle θ. Find θ to 1 decimal place.
Answer
Question 5
What is the exact value of tan 30°?
- A. 1
- B. √2/2
- C. √3/3
- D. √3
Question 6
In a right triangle, the side adjacent to a 24° angle is 11 cm. Find the hypotenuse to 1 decimal place.
Answer
Question 7
Maya flies a drone 23 m above the ground. From where Maya stands, the angle of elevation to the drone is 19°. How far horizontally is the drone from Maya? Give 1 decimal place.
Answer
Question 8
Chloe stands 76 m from the base of a tower. The angle of elevation to the top is 25°. How tall is the tower, to the nearest metre? (Ignore Chloe's height.)
Answer
Question 9
A right triangle has the side adjacent to a 60° angle equal to 9 cm. Find the side opposite the 60° angle. Give an exact answer.
Answer
Question 10
An equilateral triangle has sides of 16 cm. Find its exact height.
Answer
Question 11
In a right triangle the hypotenuse is 19 m and the side adjacent to angle θ is 17 m. Find θ to 1 decimal place.
Answer
Question 12
In a right triangle, angle θ has opposite side 8, adjacent side 15 and hypotenuse 17. What is tan θ?
- A. 17/8
- B. 8/17
- C. 15/17
- D. 8/15
Question 13
A right triangle has hypotenuse 11 cm and an angle of 45°. Find the side adjacent to the 45° angle, to 1 decimal place.
Answer
Question 14
In the right triangle, which side is the adjacent to angle θ?
- A. t
- B. q
- C. p
Question 15
A ramp rises at 43° over a horizontal distance of 11 m. How high does it rise? Give 1 decimal place.
Answer
Question 16
A 18 m ladder leans against a wall at 26° to the ground. To find how high up the wall it reaches, which ratio do you use with the 26° angle?
- A. sin
- B. cos
- C. tan
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