Answer:
Step-by-step explanation:
height = 14tan(24°)
area = 0.5(base)(height)
Find the angle that triples the height.
tanθ = 3×14tan(24°)
θ = arctan(3×14tan(24°)) ≅ 53.2°
The base angle will be 53.3 degrees when the area gets treble.
A triangle with two sides of equal length is an isosceles triangle.
The angles that have the base as one of their sides are called base angles.
[tex]Area = \frac{1}{2} bh[/tex]
Where,
b is the base of the triangle
h is the height of the triangle
According to the given question
We have,
Base angle of the isosceles triangle is 24 degrees.
Base of the isosceles triangle is 28 cm.
In triangle ABC
We have
BC = 28cm, BD = 14cm, AD = h and ∠ABD = 24 degrees
Now, in right angle triangle ABD
[tex]tan24 = \frac{h}{14}[/tex]
⇒ tan24 × 14 = h
Therefore,
Area of triangle ABC = [tex]\frac{1}{2}[/tex] × 28 × 14 × tan 24
Area of triangle ABC = 196tan24
Therefore, the base angles of an new isosceles triangle when the area get treble is given but with the same base by
Area of new isosceles = 3× area of triangle ABC
⇒ [tex]\frac{1}{2}[/tex]× 28 × tanθ × 14 = 3×196tan24
⇒tanθ = 3 × 0.4452
⇒ tanθ = 1.3356
⇒ θ = [tex]tan^{-1}(1.34)[/tex]
⇒ θ = 53.3 degrees
Hence, the base angle will be 53.3 degrees when the area gets treble.
Learn more about isosceles triangle and base angle here:
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