Question

In this triangle BD is perpendicular to AC.

10 cm BA
6 cm D 13 cm a Calculate the angle BCD. b Calculate the angle BAD. c Using your answers to part a and b, calculate the angle ABC.​

Answer 1

i.<BCD =
`24.8^(o)`

ii. <BAD =
`36.9^(o)`

iii. < ABC =
`118.3^(o)`

i. To determine the measure of angle BCD, we have;

Tan θ =
`(opposite)/(adjacent)`

Tan C =
`(6)/(13)`

= 0.46154

C =
`Tan^(-1)` 0.46154

= 24.775

C =
`24.8^(o)`

ii. To determine the measure of angle BAD, we have;

Sin A =
`(opposite)/(hypotenuse)`

=
`(6)/(10)`

Sin A = 0.6

A =
`Sin^(-1)` 0.6

= 36.87

A =
`36.9^(o)`

iii. <BCD + <BAD + <ABC = 180

24.8 + 36.9 + <ABC = 180

<ABC = 180 - 61.7

= 118.3

<ABC =
`118.3^(o)`