# Math

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In traveling across flat land, you notice a mountain in front of you. Its angle of elevation to the peak is 3.5 degrees. After you drive 13 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.

• Math - ,

Two rt triangles are formed. The common ver. side represents the ht. of
the mountain. The 3.5 deg angle of elevation lies bet. the hyp and hor side of the larger triangle. The 9 deg
angle is located bet. the hyp and hor side of the smaller triangle.

tan3.5 = h / (x + 13),
h = (x + 13)tan3.5,
h = (x + 13)0.0612,

Eq1: h = 0.0612x + 0.7951,

tan9 = h/x,
Cross multiply:
h = xtan9,

Eq2: h = 0.1584x.

Substitute 0.1584x for h in Eq1:
0.1584x = 0.0612x + 0.7951,
0.1584x - 0.0612x = 0.7951,
0.0962x = 0.7951,

x = 0.7951 / 0.0962 = 8.27.

h = 0.1584 * 8.27 = 1.31 mi = ht of mt.

• Math - ,

Emily chooses two numbers.

She adds the two numbers together and divides the rusult by 2.

One Emily's numbers is 12

what is Emily's other numbers?