Question

A mountain has a snow line at an elevation of about 9,000 feet which runs parallel to its base. From your patio, the mountain looks like a triangle. The length of the snow line is 2.4 times the height of the snow covered part of the mountain. a. If the snow covers about 1,200,000 square feet of the part of the mountain you can see, how high is the mountain? b. What percentage of the part of the mountain that you can see is covered in snow?

Answer 1

a. The height of the mountain = 1000 ft + 9000 ft = 10000 ft

b. Percentage covered with snow = 1%

Explanation:

The diagram below illustrate how the snow line formed on the triangular mountain as described.

Area of a triangle = 1/2 × base × height

The upper section of the triangle where the snow line cut, the height h can be calculated below

Area of a triangle = 1/2 × base × height

Area of a triangle = 1/2 × 2.4 h × h

1200000 = 2.4h²/2

cross multiply

1200000 × 2 = 2.4h²

2400000 = 2.4h²

divide both sides by 2.4

h² = 2400000/2.4

h² = 1000000

h = √1000000

h = 1000 ft

The height of the mountain = 1000 ft + 9000 ft = 10000 ft

b. the snow line is parallel with base of the mountain

snow line base = 2.4 × 1000 = 2400

base of the mountain = 2.4 × 10000 = 24000

area of the mountain = 1/2 × 24000 × 10000

area of mountain = 240000000/2

area of mountain = 120000000 ft²

Percentage covered with snow = 1200000/120000000 × 100

Percentage covered with snow = 120000000/120000000

Percentage covered with snow = 1%