Mathematics: What is the measure of angle a? (click for picture)

G(x)=2/5(10)-x it the last one...

What is the measure of angle a? (click for picture)

joshua9814

13.01.2022

57.5°

Step-by-step explanation:

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

$\frac{DE}{BC}$ = $\frac{AE}{AC}$ , that is

$\frac{15}{4}$ = $\frac{7+AC}{AC}$ ( cross- multiply )

15AC = 4(7 + AC)

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

11AC = 28 ( divide both sides by 11 )

AC = $\frac{28}{11}$

Using the tangent ratio in right $\frac{opposite}{adjacent}$ Δ ABC to find ∠A

cosA = $\frac{opposite}{adjacent}$ = $\frac{BC}{AC}$ = $\frac{4}{\frac{28}{11} }$ = $\frac{44}{28}$ , thus

∠A = $tan^{-1}$ ( $\frac{44}{28}$ ) ≈ 57.5° ( to 1 dec. place )

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