Answer:
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The greatest angle in the given triangle is 104 degrees.
<h3>
What is a triangle?</h3>
- The polygon with 3 sides, three vertices, and three angles is known as a triangle.
- A triangle's overall number of degrees is always 180 degrees.
Given:
- Let, the second angle has a measurement of x degrees.
- The first angle's measurement is 24 degrees greater than the second angle's measurement.
- As a result, the first angle is (24+x) degrees.
- The third angle is four times as large as the second.
- As a result, the third angle has a measure of 4x.
So,
- (24 + x) + x + 4x = 180
- 6x = 124 - 48
- 6x = 156
- x = 156/6
- x = 26
As a result, the second angle has a measurement of 26 degrees.
The first angle's measurement is now 24 degrees greater than the second angle's measurement.
Now,
As a result, the first angle has a measure of 50 degrees.
The third angle is now four times the size of the second angle.
So,
Therefore, the greatest angle in the given triangle is 104 degrees.
Know more about triangles here:
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Answer:
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Answer:
7.7 km
Explanation:
Use cosine rule as here given two sides and one angle.
Cosine rule states:
a² = b² + c² - 2bc cos(A)
While solving, treat a = 7.5 km as to that opposite angle is given of 68°
then b = missing side, c = 5.2 km, A = 68°
Applying rule:
7.5² = b² + 5.2² - 2(b)(5.2) cos(68)
56.25 = b² + 27.04 - 3.8959b
56.25 - 27.04 = b² - 3.8959b
b² - 3.8959b = 29.21
b² - 3.8959b - 29.21 = 0
apply quadratic equation, Here [a = 1, b = - 3.8959, c = -29.21]
As length cannot be negative. Hence the value of b is only 7.7 km
The measure of angle FHG = 42 degrees. This is the same as the arc length.
The measure of angle FEG = 21 degrees. This is half the value of the arc length.
