Question

I keep getting the answer of 28.89° but that’s wrong and I don’t know how to get to the right answer.

Answer 1

26.565⁰

Explanation:

Triangles AEM and BEM are congruent since
AE = BE
m∠AME = m∠BME=90°
and EM is the common side

So AM = BM = AB/2 = 16/2 = 8

Triangle EAM is a right triangle with hypotenuse AE = 17 and AM = 8

So EM² = (17² - 8²) by the Pythagorean theorem
EM² = 289 - 64 = 225
EM = √225 = 15 cm

To find m∠ECM, note that triangle ECM is a right triangle with m∠EMC = 90° and the side opposite ∠EMC = EC, the side opposite ∠ECM is EM

By the law of sines

EC/sin90 = EM/sin(∠ECM)

So,

sin(∠ECM) = EM/EC since sin 90 = 1

So we have to compute EC

Again note that the triangle MCB with sides BM, MC and BC is a right triangle with m∠CBM = 90°

The hypotenuse is MC

So MC ² = MB² + BC² = 15² + 30² = 1125

MC = √1125 = 33.54 cm

Therefore
sin(∠ECM) = EM/MC = 15/33.54 = 0.4472

m∠ECM = sin⁻¹ (0.4472)

= 26.565⁰

To be honest I am not 100% sure of this answer, please check and see if this works. Thanks

Answer 2

for (a) i got 15

Explanation:

AE=17, AB=16 which makes AM=8

so from there u do pythagorean theorem

17^2 - 8^2 = 225

√255= 15