WHAT IS THE BASE LENGTH OF AN ISOSCELES TRIANGLE IF YOU KNOW THE EQUAL SIDES HAVE A VALUE OF 5 AND THE ANGLE BETWEEN THEM IS 45 DEGREES AND THE BASE ANGLES ARE 67.5 DEGREES?
Why are you shouting?
You could use the Sine Law
let the missing side by x
x/sin45 = 5/sin67.5
x = 5sin45/sin67.5 = 3.827
you could also use the Cosine Law:
x^2 = 5^2 + 5^2 - 2(5)(5)cos45
= 50 - 35.35534
= 14.6447
x = √14.6447 = 3.827
To find the base length of an isosceles triangle, you can use the Sine Law. The Sine Law relates the lengths of the sides of a triangle to the sines of the opposite angles.
First, let's label the triangle. Assume the equal sides have a length of 5, and the angle between them is 45 degrees. Let's call this angle A. The base angles are given as 67.5 degrees each, which we can call angles B and C.
Using the Sine Law, we have:
sin(A) / a = sin(B) / b = sin(C) / c
In our case, the angle A is 45 degrees, the length of the equal sides is 5, and we want to find the length of the base, which we can denote as b.
Let's plug in the values we know:
sin(45) / 5 = sin(67.5) / b
To solve for b, we can rearrange the formula:
b = (5 * sin(67.5)) / sin(45)
Now, let's calculate it:
b = (5 * 0.9239) / 0.7071
b ≈ 6.481
Therefore, the base length of the isosceles triangle is approximately 6.481.