From a boat on the lake, the angle of elevation to the top of the cliff is 24°22'. If the base of the cliff is 747 feet from the boat, how high is the cliff (to the nearest foot)

Question

hello could you help me please i have a little problem with this trigonometry

Answer 1

a=

b=747'

c=

α=24.55°

β=

γ=90°

You want side "a".

Since there's 180° in a triangle; β=65.45°.

So, a/sinα=b/sinβ=c/sinγ

747/.909=.821=a/.415; a=341.215'

Answer 2

First we can calculate the angle in decimal degrees:

24° 22' = 24 + 22/60 = 24.367°

Since we are trying to compute the height of the cliff and we know the distance from the boat to the base of the cliff, we need to use the tangent function. In other words:

tan(θ) = opposite/adjacent

tan(24.367) = o/747

o = 747 * tan(24.367) = 338.33 ft