Question

When Mount Saint Helens erupted in 1980, the top of the mountain was blown off. A surveyor determined the height of the new summit by measuring the angle of elevation to the top to be 37°46'. She then moved 1000 feet closer to the volcano and measured the angle of elevation to be 40°30'. Find in ft the new height of Mount Saint Helens.

Answer 1

Height= 8341.6 feet

Explanation:

A surveyor determined the height of the new summit by measuring the angle of elevation to the top to be 37°46'. She then moved 1000 feet closer to the volcano and measured the angle of elevation to be 40°30'.

40°30'= 40.5°

37°46'= 37.767°

b = 180-40.5

b= 139.5°

a= 180-139.5-37.767

a= 2.733°

Using sine method

1000/Sina= y/sinB

1000/sin 2.733= y/sin 139.5

(1000*sin 139.5)/sin 2.733= y

(1000*0.6494)/0.04768= y

13619.96= y

Y= 13620 feet

Height/sin 37.767= 13620

Height=13620*sin37.767

Height= 8341.59

Height= 8341.6 feet