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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Question 1
In a right triangle, the side adjacent to a 46° angle is 9 cm. Find the hypotenuse to 1 decimal place.
Answer
Question 2
A 11 m ladder leans against a wall at 58° to the ground. To find how high up the wall it reaches, which ratio do you use with the 58° angle?
- A. sin
- B. cos
- C. tan
Question 3
An equilateral triangle has sides of 16 cm. Find its exact height.
Answer
Question 4
In a right triangle the hypotenuse is 22 m and the side adjacent to angle θ is 6 m. Find θ to 1 decimal place.
Answer
Question 5
A right triangle has two equal sides of 4 cm and a 45° angle. Find the hypotenuse. Give an exact answer.
Answer
Question 6
Daniel stands 51 m from the base of a tower. The angle of elevation to the top is 29°. How tall is the tower, to the nearest metre? (Ignore Daniel's height.)
Answer
Question 7
A ramp rises at 57° over a horizontal distance of 15 m. How high does it rise? Give 1 decimal place.
Answer
Question 8
In the right triangle, which side is the hypotenuse?
- A. u
- B. q
- C. t
Question 9
In triangle MXL, the right angle is at X. Using angle M, which side is the adjacent?
- A. XL
- B. ML
- C. MX
Question 10
A right triangle has opposite side 13 cm and adjacent side 7 cm to angle θ. Find θ to 1 decimal place.
Answer
Question 11
Grace flies a drone 26 m above the ground. From where Grace stands, the angle of elevation to the drone is 31°. How far horizontally is the drone from Grace? Give 1 decimal place.
Answer
Question 12
What is the exact value of sin 60°?
- A. √3
- B. √3/2
- C. √2/2
- D. 1
Question 13
A right triangle has hypotenuse 12 cm and an angle of 42°. Find the side opposite the 42° angle, to 1 decimal place.
Answer
Question 14
In a right triangle you know angle θ and the hypotenuse. You want the opposite side. Which ratio should you use?
- A. sin
- B. cos
- C. tan
Question 15
In a right triangle, angle θ has opposite side 7, adjacent side 24 and hypotenuse 25. What is cos θ?
- A. 24/7
- B. 25/7
- C. 7/25
- D. 24/25
Question 16
From the top of a 57 m cliff, the angle of depression to a boat is 28°. How far is the boat from the foot of the cliff? Round to the nearest metre.
Answer
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