Question

What is the measure of angle A? (Click for picture)

Answer 1

57.5°

Explanation:

Δ ADE and Δ ABC are similar, thus the ratios of corresponding sides are equal, that is

`(DE)/(BC)` =
`(AE)/(AC)`, that is

`(15)/(4)` =
`(7+AC)/(AC)` ( cross- multiply )

15AC = 4(7 + AC)

15AC = 28 + 4AC ( subtract 4AC from both sides )

11AC = 28 ( divide both sides by 11 )

AC =
`(28)/(11)`

Using the tangent ratio in right
`(opposite)/(adjacent)`Δ ABC to find ∠A

cosA =
`(opposite)/(adjacent)` =
`(BC)/(AC)` =
`(4)/((28)/(11) )` =
`(44)/(28)`, thus

∠A =
`tan^(-1)`(
`(44)/(28)`) ≈ 57.5° ( to 1 dec. place )