APPLYING TRIGONMETRY-A forest ranger spots a bear in the distance from her 10 meter tower,?

Question

The angle of depression is 30 degress. How far away is the bear form the base of the tower?

Answer 1

Draw a right angled triangle, ABC ,right angled at B
A is top of tower
B is base of tower
BC is horizontal
/_ABC = 30°

tan 30° = 10 / BC
BC = 10 / tan 30°
BC = 10 / (1 / √3)
BC = 10 √3

Bear is 17.3 m from base of tower.

Answer 2

1) draw a diagram.

2) let x be distance of bear from base of tower.

3) angle of depression is measured from a line parallel to ground, 10 meters above ground.

4) sin (30) = 10/h, h is hypotenuse
1/2 = 10/h, so h = 20 meters.

5) triangle has base x, height 10, hypotenuse 20.

6) Pythagorean theorem.:

x^2 + 10^2 = 20^2 or
x^2 = 400 - 100
x^2 = 300
x = sqrt(300) or
= 10 sqrt(3).

Done.

Answer 3

Hi,

use this formula -

tan(angle) = y / x (in other words, opposite over adjacent).
y = 10 m
(angle) = 30,
tan(30) = 0.57735 = 10 / x
isolate the x variable
x = 10 / 0.57735 = 17.32 meters.

Answer 4

draw a picture first. then use sine, cosine or tangent to find the answer. Remember SOH CAH TOA: sine is opposite/adjacent; cosine is adjacent over hypotenuse; tangent is opposite over adjacent. i think it would be like tan30=x/10 put the tan30 over 1 and solve it like a proportion.

tan30/1=x/10; x=tan300; you can solve tan300 using your calc.

im pretty much positive thats right, this was the only part of geometry i understood haha.