Question

The Sine and Cosine Rules
Right-angled triangle Trigonometry
Please note your working out with your answer, thank you.

Q11) A lifeguard on top of an observation tower 12.5m high notices a surfer in trouble at an angle of depression of 8 degrees. How far, correct to one decimal place, is the surfer from the tower?

Q13) A boat is 420m from the base of the cliff. The angle of depression of the boat from the top of the cliff is 28 degrees. Find the height of the cliff to the nearest metre.

Answer 1

Hello,
I am not doing that with sin, cos and pythagorean theorem.

DEFINITION: we call TAN x=sin x / cos x
This means that in a right triangle the tangent of an angle is the ration of opposed side by adjacent side.

11: tan 8°=12.5/d
==>d=12.5/tan 8°=12.5/0.14054...=88.942121...m≈88.9 (m)

12:
tan 28°=h/420
==>h=420*tan 28°=420*0.5317...=223.3179...≈223.3 (m)