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
so
∠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
so
∠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
so
∠EBC+102.9°+41°=180°
∠EBC=180°-143.9°
∠EBC=36.1°
