From the top of a lighthouse 190 ft high, the angle of depression of a boat out at sea is 34º.
Find the distance from the boat to the foot of the lighthouse to the
nearest tenth of a foot.

Step-by-step explanation:

= 412

feet

Explanation:

The angle of depression is always measured from the horizontal.

A triangle is formed by the lighthouse, the ground and the boat. The angle of depression is not in the triangle, but it is equal to the angle of elevation at the boat. (Alternate angles on parallel lines)

The angle at the top of the lighthouse, inside the triangle is:

90

°

−

27

°

=

63

°

The distance to the boat is the side opposite the angle of

63

°

while the height of the lighthouse is the adjacent side.

opposite

adjacent

=

tan

63

°

distance

210

=

tan

63

°

distance

=

210

×

tan

63

°

=

412

feet

your answer is d 2,500

step-by-step explanation:

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.