Suppose Romeo is serenading Juliet while she is on her balcony. Romeo is facing north and sees the balcony at an angle of elevation of 20 degrees. Paris, Juliet's other suitor, is facing west and sees the balcony at an angle of elevation of 18 decrees. Romeo and Paris are 100 m apart on the ground. Determine the height of Juliet's balcony above the ground. |
Let Juliet's point be J. We'll call the point on the ground directly below Juliet G. Romeo is at point R. Paris is at point P. Let the length of RG = r. Length of PG=p. Length of GJ = h. (how high Juliet is) since RP, RG and PG are a right triangle: r^2+p^2=100^2 We also know tan(20) = h/r tan(18)=h/p so: r=h/tan(20) p=h/tan(18) r^2+p^2=100^2 (h/tan(20))^2 + (h/tan(18))^2 =100^2 h^2*((1/tan(20))^2+(1/tan(18))^2) = 100^2 h^2 = 100^2/((1/tan(20))^2+(1/tan(18))^2) h = sqrt(100^2/((1/tan(20))^2+(1/tan(18))^2) ) To calculate in Algebra Calculator: we convert degrees to radians by multiplying the degrees by PI/180 sqrt(100^2/((1/tan(20PI/180))^2+(1/tan(18PI/180))^2) ) =24.2 meters (approx) |