Answer:
The height of the mountain is 2305 feet.
Step-by-step explanation:
Given that:
We are provided with the angles are in degree, minutes and seconds, we are required to convert them back to degrees.
So, 47°57′52″ in degrees only will be :
=[tex]47^0 + 57 \times \dfrac{1}{60}+ 52 \times \dfrac{1}{3600}[/tex]
= [tex]47^0 +0.95^0+0.0144^0[/tex]
= 47.9644°
[tex]\simeq[/tex] 47.96°
For the second angle after he walked a distance if 1374 feet; we have:
73°3′35″
= [tex]73^0 + 3 \times \dfrac{1}{60} \times 35 \times \dfrac{1}{3600}[/tex]
= [tex]73^0 + 0.05 ^0 \times 0.0097^0[/tex]
= 73.000485°
[tex]\simeq[/tex] 73
From the image attached below;
x = 180° - 73° = 107° ( angles on a striaght line)
107° + 47.96° + y = 180° ( sum of angles in a triangle)
y = 180° - 107° - 47.96°
y = 25.04
Using sine rule:
[tex]\dfrac{a}{sin \ 47.96} = \dfrac{1374}{sin \ 25.04}[/tex]
a × sin 25.04 = 1374 × sin 47.96
[tex]a = \dfrac{ 1374 \times sin \ 47.96} { sin \ 25.04 }[/tex]
[tex]a = \dfrac{ 1020.439} {0.4233}[/tex]
a = 2410.68
From the figure, using trigonometry rule;
[tex]Sin 73 = \dfrac{h}{a}[/tex]
[tex]Sin \ 73 = \dfrac{h}{2410.68}[/tex]
h = sin 73 × 2410.68
h = 0.9563 × 2410.68
h = 2305.33 feet
To the nearest whole number , the height is 2305 feet.
