d) The elevation of the top of a tower of height 60 m from two places on the samp thorizontal ine due west of it are \( 60^{\circ} \) and \( 45^{\circ} \). Find the distance between th two places.

To find the distance between the two places, you can use the height of the tower and the angles of elevation. For the first point where the angle of elevation is \(60^{\circ}\): Using the tangent function: \[ \tan(60^{\circ}) = \frac{60}{d_1} \implies d_1 = \frac{60}{\sqrt{3}} \quad (\text{since } \tan(60^{\circ}) = \sqrt{3}) \] For the second point where the angle of elevation is \(45^{\circ}\): \[ \tan(45^{\circ}) = \frac{60}{d_2} \implies d_2 = 60 \quad (\text{since } \tan(45^{\circ}) = 1) \] The distance between the two places will then be: \[ \text{Distance} = d_1 + d_2 = \frac{60}{\sqrt{3}} + 60 = 60\left(1 + \frac{1}{\sqrt{3}}\right) \] Calculating it gives approximately 60(1.577) which is about 94.62 m. Thus, the distance between the two places is approximately 94.62 meters.