Answer:
Measure of base angles = 77.5 °
Base of the triangle = 40.52cm
Step-by-step explanation:
Solution:
** Get the base angles:
We know that the total measurement interior angles of triangle is equivalent to 180°. Given that one of the angles is 25°, subtract that from 180°.
180 - 25 = 155
In isosceles triangle, the base angles are congruent since the two sides are equal so divide 155 by 2 to get the measurements of each base angles.
155/2 = 77.5°
**To get the measurement of base:
Cut the triangle in the middle forming 2 right triangles and then get the measurement of the height using the measurement of base angle and the leg
sin 77.5 = height / leg
sin 77.5 = height / 40
40 sin 77.5 = 34.49
Then using the Pythagorean theorem, solve for the base.
Pythagorean theorem formula:
c^2 = a^2 + b2
where
c = hypotenuse (leg/side)
a = longer side
b = shortest side
40² = 34.49² + b²
40² - 34.49² = b²
1600 - 1189.56 = b²
410.44 =b²
b = √410.44
b = 20.26
Since that is only the half of the base, multiply it by 2 to get the whole measurement of the base
20.26 x 2 = 40.52cm
Hope you understand the explanation and this could help you =)
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Answers & Comments
Answer:
Measure of base angles = 77.5 °
Base of the triangle = 40.52cm
Step-by-step explanation:
Solution:
** Get the base angles:
We know that the total measurement interior angles of triangle is equivalent to 180°. Given that one of the angles is 25°, subtract that from 180°.
180 - 25 = 155
In isosceles triangle, the base angles are congruent since the two sides are equal so divide 155 by 2 to get the measurements of each base angles.
155/2 = 77.5°
**To get the measurement of base:
Cut the triangle in the middle forming 2 right triangles and then get the measurement of the height using the measurement of base angle and the leg
sin 77.5 = height / leg
sin 77.5 = height / 40
40 sin 77.5 = 34.49
Then using the Pythagorean theorem, solve for the base.
Pythagorean theorem formula:
c^2 = a^2 + b2
where
c = hypotenuse (leg/side)
a = longer side
b = shortest side
40² = 34.49² + b²
40² - 34.49² = b²
1600 - 1189.56 = b²
410.44 =b²
b = √410.44
b = 20.26
Since that is only the half of the base, multiply it by 2 to get the whole measurement of the base
20.26 x 2 = 40.52cm
Hope you understand the explanation and this could help you =)