I am in the 10th Grade and my question is: The base of an isosceles triangle is 21cm. long. The altitude to the base is 9cm. long. What is the approx. measure of a base angle of the triangle?
The tangent of that angle is 9/10.5 = 0.8571
Trigonometric tables will tell you that the angle is 40.6 degrees.
How did you get 9/10.5 from the problem?
Never mind I got it now. Thanks for the help!!!
To find the approximate measure of the base angle of an isosceles triangle, we need to use the tangent ratio. The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.
In this case, the given information tells us that the altitude (which is the height) to the base is 9 cm long. This side is the opposite side to the base angle. The length of the base itself is given as 21 cm, which is the adjacent side to the base angle.
So, we can set up the equation: tangent(angle) = 9/21 = 0.8571
To find the measure of the angle, we need the inverse tangent (also known as arctangent or tan^(-1)) function. The arctangent of 0.8571 will give us the approximate measure of the angle.
Using a calculator or a trigonometric table, the arctangent of 0.8571 is approximately 40.6 degrees.
Therefore, the approximate measure of the base angle of the triangle is 40.6 degrees.