A simple measuring device is used at points X and Y on the same horizontal level to measure the angles of elevation of the peak P of a certain mountain. If X is known to 5,200m above sea level, /XY/ = 4,000m and the measurements of the angles of elevation of P at X and Y are 15° and 35° respectively, find the height of the mountain. (Take (tan 15 = 0.3) and (tan 35 = 0.7))
Explanation
In (Delta) BPY, (tan 35° = frac{h}{x})
(h = x tan 35 = 0.7 x … (1))
In (Delta) BPX, (frac{h}{x + 4000} = tan 15)
(frac{h}{x + 4000} = 0.3)
(h = 0.3 (x + 4000) = 0.3x + 1200 … (2))
Equating (1) and (2) as the values of h, we have
(0.7x = 0.3x + 1200 implies 0.7x – 0.3x = 1200)
(0.4x = 1200 times x = frac{1200}{0.4} = 3000m)
(therefore h = 0.7x = 0.7 (3000) = 2100m)
(text{The total height = } 5200m + 2100m = 7300m)