Free examples and worked answers. No account needed.
Practise the method.
Reverse ratios and multi-step lengths
Reverse ratios and multi-step lengths
Example 1
In a right triangle, the leg adjacent to a 60∘ angle is 7cm. Find the hypotenuse x, in cm. Use cos60∘=0.5.
Right triangleDiagram not to scaleShow worked answer
Answer: 14
cos60∘=hypotenuseadjacent=x7.
Thus x=07.5=14cm.
Example 2
A vertical flagpole is 6m tall. The angle of elevation of its top from level ground is 45∘. Find the horizontal distance x to its base, in m. Use tan45∘=1.
Right triangleDiagram not to scaleShow worked answer
Answer: 6
tan45∘=distanceheight=x6
x=16=6m.
Example 3
An observer's eye is 3m above level ground and 8m horizontally from a tower. The angle of elevation to the top is 45∘. Find the tower's full height, in m. Use tan45∘=1.
Right triangleDiagram not to scaleShow worked answer
Answer: 11
Height above the eye=8×tan45∘=8m.
Add eye height: 8+3=11m.
Put it into practice.
Sign in to choose a set, get feedback and keep your progress.