Someone !1. a person at ground level measures the angle of elevation to the top of a building to be 74°. if at this point the person is 34 feet away from the base of the building, then how tall is the building? round to the tenths place. show work/steps and provide units with your answer. 2. in right triangle pqr, p and q are complementary angles. the value of sin q is 9/ . what is the value of cos p? a.9/41 b.41/9 c.40/41 d/41/40

(1) See below for a diagram. Basically, the distance on the ground from the person to the building (34 ft) is adjacent to the angle of elevation (74 degrees) and the height of the building (labeled h in the diagram) is the side opposite the angle. Since we are dealing with opposite and adjacent we use the tangent of the angle and tan = opp/adj

Specifically,
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feet.

Please be sure your calculator is set to degrees (not radians) when you do this problem.

(2) Here since P & Q are complimentary it means that their sum is 90 degrees. Since this is a right triangle that means that the remaining angle (R) must be the right angle. See below for a diagram.

sin = opp/hyp. As the sin Q =  9/41 this means that 9 is the length of the side opposite Q (the side PR) and 41 is the length of the hypotenuse. This makes the remaining side (QR) 40 in length.

cos = adj/hyp. If we focus on angle P the side adjacent (next to) is 9 and the hypotenuse is 41. Thus the cos of P = 9/41.

You could have also realized that if P & Q are complimentary the sin P = cos Q and the cos P = sin Q. We were not asked about tangent but it is also the case that tan P = cot Q and cot P = tan Q.

25 inches - 0.694 yards