Simplify 5(cis7pi/4)^4
1 answer:
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<u>Given</u>:
Given that the isosceles trapezoid JKLM.
The measure of ∠K is 118°
We need to determine the measure of each angle.
<u>Measure of ∠L:</u>
By the property of isosceles trapezoid, we have;
Thus, the measure of ∠L is 62°
<u>Measure of ∠M:</u>
By the property of isosceles trapezoid, we have;
Substituting the value, we get;
Thus, the measure of ∠M is 62°
<u>Measure of ∠J:</u>
By the property of isosceles trapezoid, we have;
Substituting the value, we get;
Thus, the measure of ∠J is 118°
Hence, the measures of each angles of the isosceles trapezoid are ∠K = 118°, ∠L = 62°, ∠M = 62° and ∠J = 118°
Answer:the height of the balloon is 670.244 feet
Step-by-step explanation:
The right angle triangle BLD represents the scenario.
h represents the height of the balloon.
We would apply trigonometric ratio to determine h.
Tan # = opposite side/adjacent side
Looking at triangle LCD,
# = 61 degrees
h = opposite side
x = adjacent side
Tan 61 = h/x
1.7321 = h/x
h = 1.7321x
Looking at triangle LBD,
# = 54 degrees
h = opposite side
x + 100 = adjacent side
Tan 54 = h/x + 100
1.3764 = h/x + 100
h = 1.3764(x + 100)
Therefore,
1.7321x = 1.3764(x + 100)
1.7321x = 1.3764x + 137.64
137.64 = 1.7321x - 1.3764x
137.64 = 0.3557x
x = 137.64/0.3557 = 386.955
h = 1.7321x = 386.955 × 1.7321
h = 670.244 feet
