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3 years ago

NEED HELP 50 POINTS!! WILL MARK BRAINLIEST ANSWER. Find the lengths of all the sides and the measures of the angles.

Mathematics

1 answer:

Sergeeva-Olga [200]3 years ago

3 0

Answer:

Part 1) ∠ABD=23.9°

Part 2) ∠ADB=119.1°

Part 3) AB=506.7 ft

Part 4) ∠BDE=60.9°

Part 5) ∠BED=77.1°

Part 6) DE=239.6 ft

Part 7) BE=312.8 ft

Part 8) ∠BEC=102.9°

Part 9) ∠EBC=36.1°

Step-by-step explanation:

Let

A-----> Zebra house

B ----> Entrance

C ----> Tiger house

D ---> Giraffe house

E ----> Hippo house

see the attached figure with letters to better understand the problem

step 1

In the triangle ABD

Find the measure of angle ABD

Applying the law of sines

sin(37°)/349=sin(ABD)/235

sin(ABD)=235*sin(37°)/349

sin(ABD)=0.4052

∠ABD=arcsin(0.4052)=23.9°

step 2

In the triangle ABD

Find the measure of angle ADB

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

∠ADB+23.9°+37°=180°

∠ADB+23.9°+37°=180°-60.9°

∠ADB=119.1°

step 3

In the triangle ABD

Find the measure of side AB

Applying the law of sines

sin(37°)/349=sin(119.1°)/AB

AB=349*sin(119.1°)/sin(37°)

AB=506.7 ft

step 4

In the triangle BDE

Find the measure of angle BDE

we have

∠BDE+∠ADB=180° ----> by supplementary angles

∠ADB=119.1°

substitute

∠BDE+119.1°=180°

∠BDE=180°-119.1°

∠BDE=60.9°

step 5

In the triangle BDE

Find the measure of angle BED

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

∠BED+60.9°+42°=180°

∠BED=180°-102.9°

∠BED=77.1°

step 6

In the triangle BDE

Find the measure of side DE

Applying the law of sines

sin(77.1°)/349=sin(42°)/DE

DE=349*sin(42°)/sin(77.1°)

DE=239.6 ft

step 7

In the triangle BDE

Find the measure of side BE

Applying the law of sines

sin(77.1°)/349=sin(60.9°)/DE

BE=349*sin(60.9°)/sin(77.1°)

BE=312.8 ft

step 8

In the triangle BEC

Find the measure of angle BEC

we have

∠BEC+∠BED=180° ----> by supplementary angles

∠BED=77.1°

substitute

∠BEC+77.1°=180°

∠BEC=180°-77.1°

∠BEC=102.9°

step 9

In the triangle BEC

Find the measure of angle EBC

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

∠EBC+102.9°+41°=180°

∠EBC=180°-143.9°

∠EBC=36.1°

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