Trigonometry Practise 2 - Mrs. Maharaj

Transcription

1 Trigonometry Practise 2 - Mrs. Maharaj Question 1 Question 2 Use a calculator to evaluate cos 82 correct to three decimal places. cos 82 = (to 3 decimal places) Complete the working to find the value of to two decimal places. y rounded tan 35 = tan 35 = y y = (to 2 dp) Question 3 Question 4 Calculate the value of b = (to 2 decimal places) b correct to two decimal places. Calculate the value of p = (to 1 decimal place) p correct to one decimal place. Question 5 Question 6 The diagonal of a rectangle makes an angle of 37 with the longer side which has a length of 10 m. Calculate the shorter side of the rectangle correct to two decimal places. Calculate the value of q correct to two decimal places. Shorter side length = m (to 2 dp) q = (to 2 decimal places)

2 Question 7 Question 8 A sailor on a boat, 1.1 km out to sea, measured the angle of elevation of the top of a cliff as 22. Calculate the height of the cliff in one decimal place. metres, correct to Height = m (to 1 decimal place) A flagpole has a support cable attached to the ground 3.5 from the base of the pole. The cable makes an angle of 64 with the ground. Calculate the height of the pole, correct to two decimal places. Height = m (to 2 decimal places) Question 9 Question 10 By looking at the sides of the triangle, what can you say about φ? An isosceles triangle has base angles of 63 and 2 sides equal to 20 cm. Find the area of the triangle correct to the nearest square centimetre. a) φ must be larger than 45 b) φ must be smaller than 45 Area = 2 cm (to nearest square cm)

3 Question 11 Question 12 A rectangle measures 8.5 cm by 4.5 cm. Calculate the size of the smaller angle made by the diagonal at the vertex of the rectangle. Smaller angle = (to the nearest degree) Complete the solution to calculate the size of angle A to the nearest degree. sin A = A = (to the nearest whole degree) Question 13 Question 14 Use or to find the size of the angle. tan β = 3.5 β = (correct to nearest whole degree) Which statement could you use to calculate the size of the acute angle θ? a) cos θ = b)tan θ = c) cos θ = d)tan θ =

4 Question 15 Question 16 For this triangle, which trig ratio is equal to the Which statement could you size of the acute angle φ? a) 1 φ = sin b) 1 φ = cos not use to calculate the fraction? a) sin φ b)cos φ c) tan φ c) 1 φ = tan Question 17 Question 18 For this triangle, which trig ratio is equal to the fraction? a) sin ω b)cos ω c) tan ω What ratio could be used to find t, the height of the tower? a) sin 27 = b)cos 27 = c) tan 27 =

5 Question 19 Question 20 Which ratio could be used to find the angle of elevation, β, from the ship to the person? a) sin β = b)cos β = c) tan β = An observatory window is 35 m above the ground. The front gate of a property can be seen through the window and is 150 m away along the flat path. Calculate the angle of depression from the observatory to the gate to the nearest degree. β = (to nearest degree) Question 21 A fishing boat skipper detected a school of fish through an angle of depression of 4. After travelling for 300 m the boat was directly over the fish. Calculate the depth of the fish to the nearest metre. Question 22 Two students in separate schools along the highway took the angle of elevation of a plane flying between them to be 25 and 31. The plane was flying 0.7 km above the ground. The plane is north of one school and south of the other. Depth = m Calculate the distance between the students in kilometres correct to 2 decimal places. Distance = km

6 Question 23 Question 24 A helicopter rose h m from the deck of an aircraft carrier and travelled 1200 m in a straight line. The angle of depression of the ship from the helicopter was then 5. Calculate the length of the shadow a 45 m high chimney stack casts when the angle of elevation to the sun is 32. Calculate Height = h, the height risen, to the nearest metre. m (to nearest metre) Write your answer correct to the nearest metre. Length = m (to nearest m) Question 25 Question 26 z = Which test should you use to show these two triangles are similar? a. b. c. d. All three pairs of corresponding sides are in the Two pairs of corresponding sides are in the same ratio and the included angles are equal. Two angles of one triangle equal two angles in the other triangle. The hypotenuses of two right-angled triangles and another pair of corresponding sides are in the

7 Question 27 Question 28 Which similarity test should be used to show these two triangles are similar? The two triangles are similar. k = = a. b. c. d. All three pairs of corresponding sides are in the Two pairs of corresponding sides are in the same ratio and the included angles are equal. Two angles of one triangle equal two angles in the other triangle. The hypotenuses of two right-angled triangles and another pair of corresponding sides are in the Question 29 Question 30 Which of these triangles are similar? a. A and B b. B and C v = c. A and C d. The three triangles are similar.