Question

At an angle of elevation 610

Answer 1

Answer:

The height of the cliff CD is approximately 539.76 m

Step-by-step explanation:

The given parameters are;

The first angle of elevation with which the captain sees the person on the cliff = 61°

The second angle of elevation with which the captain sees the person on the cliff after moving 92 m closer to the cliff = 69°

The angle made by the adjacent supplementary angle to the second angle of elevation = 180° - 69° = 111°

∴ Whereby, the rays from the first and second angle of elevation and the distance the ship moves closer to the cliff forms an imaginary triangle, we have;

The angle in the imaginary triangle subtended by the distance the ship moves closer to the cliff = 180° - 111° - 61° = 8°

By sine rule, we have;

AB/(sin(a)) = BC/(sin(c))

Which gives;

92/(sin(8°)) = BC/(sin(61°))

BC = (sin(61°)) × 92/(sin(8°)) ≈ 578.165 m

BC ≈ 578.165 m

The height CD = BC × sin(69°)

∴  The height of the cliff CD = 578.165 m × sin(69°) ≈ 539.76 m.

The height of the cliff CD ≈ 539.76 m.