Question

ΔDEF is an isosceles triangle with base angles E and F. What is the angle measure of the smallest angle in the triangle? Approximate to the nearest degree. degrees

Answer 1

We have ∠D, ∠E, and ∠F and side $d$, side $e$, and side $f$ as shown in the diagram below

by Cosine rule, we work out the angle D

$d^{2}= e^{2} + f^{2} -2(e)(f)cos(D)$
$3^{2}= 12^{2}+ 12^{2} -2(12)(12)cos(D)$
$9=144+144-288cos(D)$
$9=288-(288cos(D))$
$9-288=-288cos(D)$
$-279=-288cos(D)$
$\frac{-279}{-288}=cos(D)$
$D= cos^{-1} ( \frac{279}{288})$
$D=14.36$ rounded to 2 dp

Triangle DEF is an isosceles triangle, so we can work out ∠E and ∠F by using the angles in triangle rules

180°-14.36 = 165.64°
165.64°÷2=82.9° rounded to 1 dp

so now we have
∠D = 14.36
∠E = ∠F = 82.9

Smallest angle is angle D

Answer 2

Answer:D is 14 degrees and E and F are 83 degrees.

Step-by-step explanation: