In traveling across flat land, you see a mountain directly in front of you. its angle of elevation (to the peak) is 3.5°. after you drive 15 miles closer to the mountain, the angle of elevation is 9° (see figure). approximate the height of the mountain. (round your answer to one decimal place.)

To solve such problems we must know about Tangent (Tanθ).

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

The height of the mountain is 1.495 miles.

Given to us

Equating CD,

Substituting the value of x

Hence, the height of the mountain is 1.495 miles.

Learn more about Tangent (Tanθ) function:

link

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.

step-by-step explanation:

assume that you have 3 different side lengths.   apply the pythagorean theorem here:   square each of the two shortest sides; call them a and b, so that their squares are a² and b².   also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.