Question

Determine the height of a mountain if the elevation of the top at an unknown distance from the base is 30 and at a distance 10 km further off from the mountain along the same line the angle of elevation is 15⁰

Answer 1

Step-by-step explanation:

Let AB be the mountain of height h kilometer . Let C be point at a distance of x km . from the base of the mountain such that the angle of elevation of the top at C is 30

∘

. Let D be a point at a distance of 10 km from C such that the angle of elevation at D is of15

∘

In △ CAB , we have

tan30

∘

=

AC

AB

⇒

3

1

=

x

h

⇒x=

3h

In △ DAB we have

tan15

∘

=

AD

AB

⇒0.27=

x+10

h

⇒ (0.27) (x + 10) = h

substituting x =

3h

obtained from equation (i) in equation (ii) we get

0.27 (

3h

+ 10) = h

⇒0.27×10=h−0.27×

3h

⇒ h (1 - 0.27 ×

3

) = 2.7

⇒ h (1 - 0.46 ) = 2 . 7

⇒h=

0.54

2.7

= 5

Hence , the height of the mountains is 5 km