# Math Help - Angles problems

1. ## Angles problems

The angle of depression of a boat 50m from the base of a cliff is 30degree. How high is the cliff? Give your answer correct to 3 decimal places.

2. Hello, sakibniaz!

Did you make a sketch?

The angle of depression of a boat 50m from the base of a cliff is 30°.
How high is the cliff? . Give your answer correct to 3 decimal places.
Code:
    A * - - - - - - - - - - D
|  *  30°
|     *
|        *
h |           *
|              *
|                 *
|                30° *
C *-----------------------* B
: - - - - 50  - - - - - :

The cliff is: $h = AC$

The boat is at $B\!:\;\;\angle DAB = 30^o$
.Hence: . $\angle ABC = 30^o$

In right triangle $ACB\!:\;\;\tan 30^o \:=\:\frac{h}{50}$

Now solve for $h.$