II Solve each of the following applications Show all equa i

II. Solve each of the following applications. Show all equa i. In right triangle ABC with right angle at C, A 230, the angle of elevation at D to point B is 41° and AD = 70 meters. Solve for the length of side BC, a, in the diagram shown. (Hint: One way to solve the problem is to start with AABD to find c B or y, then use AABC or ABCD to find a.) 3. Gi 6-6 of the (Hint: the an angle the su 23° A 70 m D 41° The length of side a is

Solution

applying tan rule on 1st triangle

tan 41 = a/x

a = tan 41 * x

applying tan rule on 2nd triangle

tan 23 = a / (70 + x)

a = tan 23 (70 + x)

setting the 2 equations equal to each other

tan 41 x = tan 23 ( 70 + x)

x ( tan 41 - tan 23 ) = 70 tan 23

x = 66.80

a = tan 41 ( 66.80)

a= 58.07

length of side a = 58.07 metres