In trigonometry you are required to be able to use the theorem of Pythagoras and the trigonometric ratios (sin A, cos A, tan A) to solve problems involving right angled triangles.
Sample question 1
Seán makes a clinometer using a protractor, a straw, a piece of thread and a piece of plasticine (used as a weight). He stands 10 m from a tree and uses his clinometer to measure the angle of elevation to the top of the tree as shown. Seán is 1.75 m in height.
(a) Find the angle of elevation by reading the clinometer above.
(b) Calculate the height h as shown in the diagram. Give your answer correct to two decimal places.
(c) Find the total height of the tree.
21.45 + 1.75 = 23.2 m
(d) Another student uses the same method as Seán and finds the height of the tree to be 23.1 m. Seán did not get this answer. Give one possible reason why the answers might be different.
Answer: He could have read the angle differently, he could have taken 64˚.
Sample question 2
Vera is standing on level ground beside a building on a sunny day. She is 1.6 m tall. Her shadow is 0.5 m in length. The building casts a shadow which is 6.2 m long.
(a) Draw two triangles to show this.
(b) Explain how this information can be used to find the height of the building.
Both triangles are right-angled and the angle of elevation is the same as it is the angle of elevation of the sun. Hence the triangles are similar and the corresponding sides are in proportion, this can be used to finding the height of the building.
(c) Find the height of the building.
(d) Find the angle of elevation of the sun, correct to the nearest degree.