Since ∆AFB is similar to ∆ABC.
- < F = < B (corresponding angle)
- < G = < C (corresponding angle)
- < A = common.
<u>In </u><u>∆</u><u>A</u><u>BC,</u>
⇛< A + < B + < C = 180°
⇛37° + 65° + < C = 180°
⇛102° + < C = 180°
⇛< C = 78°
We know that, < AGF / < G = < C
So, Measure of angle < AGF = <u>7</u><u>8</u><u>°</u><u> </u><u>(</u><u>ans)</u>
7900 79 times 100 ------------
180-34=146
146-5=141
ratio=1:4
1+4=5
141÷5=28.2
x=28.2
y=112.8
I may be wrong, ask for more opinions
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The correct answer is
the flagpole is <span>
33 feet high</span>.
Explanation:
Please refer to the attached picture.
We know:
CD = 40 feet
AC = 5 feet
∠BDC = α = 35°
Using trigonometry, we know that the definition of the tangent of an angle is the ratio between the opposite side and the adjacent side, therefore:
tan α = BC / CD
Solving for BC:
BC = CD · <span>tan α
= 40 </span>· tan (35)
= 28 feet
In order to find the height of the flagpole, we need to add the distance of the clinometer from the ground:
AB = BC + AC
= 28 + 5
= 33
Hence, the flagpole is
33 feet high.
Answer:
Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°
Step-by-step explanation:
To find the measure of Angle a, we add 55 and 45, then subtract the sum from 180.
180 - 100 = 80
Angle a is 80°.
Then, we solve for Angle b. Line segment CD is congruent to Line AB, so Angle b is congruent to 55°.
After that, we find Angle c. Line segment AC is congruent to Line segment BD, so Angle c is congruent to 45°.
Lastly, we solve for Angle d using the same method we used for Angle b and Angle c. Angle d is congruent to Angle a, so it measures 80°.
So, Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°.
