for this triangle, determine tan A. then determine the measure of angle A.
h ttps://upload.wikimedia.org/wikipedia/commons/6/6f/Rtriangle.svg
side a is 1.3
side b is 2.5
If this is a rt. triangle:
Tan A = b/a.
A =
tan (A)=1.3/2.5
A=27.4744
To find tan A and the measure of angle A, we need to use the given information about the triangle. Let's follow the steps below:
1. Identify the right triangle: From the image you provided, we can see that this is a right triangle because one of the angles forms a 90-degree angle (marked by a square).
2. Label the sides: In a right triangle, the side opposite the right angle is called the hypotenuse (labeled as c), while the other two sides are called the legs (labeled as a and b).
In this case, side a is given as 1.3 and side b is given as 2.5.
3. Use the Pythagorean theorem: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse (side c) as follows:
c² = a² + b²
c² = (1.3)² + (2.5)²
c² = 1.69 + 6.25
c² = 7.94
Taking the square root of both sides, we get:
c ≈ √7.94
c ≈ 2.82
So the length of the hypotenuse (side c) is approximately 2.82.
4. Determine tan A: Tangent (tan) of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle (in this case, side a) to the length of the side adjacent to the angle (in this case, side b).
tan A = a / b
tan A = 1.3 / 2.5
tan A ≈ 0.52
So tan A is approximately 0.52.
5. Determine the measure of angle A: To find the measure of angle A, we need to use the inverse tangent (arctan) function.
Angle A = arctan(tan A)
Angle A = arctan(0.52)
Angle A ≈ 27.6 degrees
Therefore, the measure of angle A is approximately 27.6 degrees.