Let (feet) and (feet) be the heights of the and lower parts of the radio tower. We have z1 z2 tan (36°) = =>z1 = 400 tan (36°) ft tan (23°) = =>z2 = 400 tan (23°) ft So the height of the tower is z1 + z2 = 400 tan (36°) + 400 tan (23°) 460.4069 ≈ ft. 15. Let x (feet) be the distance from the person to the monument, (feet) and (feet) be the heights a b of the upper and lower parts of the building.We have tan (15°) = =>a = tan (15°) x and tan (2°) = =>b = tan (2°) x Since 200 = + = tan (15°) + tan (2°) = [tan (15°) + tan (2°)] a b x x x Thus the distance from the person to the monument is = 660.3494 ft. x ≈ 17. Since tan (40°) = , the height from the base to the top of the building is 300 tan (40°) ft. Since tan (43°) = , the height from the base to the top of the antenna is 300 tan (43°) ft. Therefore, the height of the antenna = 300 tan (43°) - 300 tan (40°) 28.0246 ft. ≈ 19. We have tan (63°) = =>a = tan (39°) = =>b = Therefore = + = + 143.04265. x a b ≈ 21.
Let z1 (feet) and z2 (feet) be the heights of the and lower parts of the radio tower. We have tan (36°) = =>z1 = 400 tan (36°) ft tan (23°) = =>z2 = 400 tan (23°) ft So the height of the tower is z1 + z2 = 400 tan (36°) + 400 tan (23°) ≈ 460.4069 ft. 15. Let x (feet) be the distance from the person to the monument, a (feet) and b (feet) be the heights of the upper and lower parts of the building.We have tan (15°) = =>a = x tan (15°) and tan (2°) = =>b = x tan (2°) Since 200 = a + b = x tan (15°) + x tan (2°) = x [tan (15°) + tan (2°)] Thus the distance from the person to the monument is x = ≈ 660.3494 ft. 17. Since tan (40°) = , the height from the base to the top of the building is 300 tan (40°) ft. Since tan (43°) = , the height from the base to the top of the antenna is 300 tan (43°) ft. Therefore, the height of the antenna = 300 tan (43°) - 300 tan (40°) ≈ 28.0246 ft. 19. We have tan (63°) = =>a = tan (39°) = =>b = Therefore x = a + b = + ≈ 143.04265. 21.