suppose triangle ABC has right angle C. find the measures of the other sides to the nearest whole number.
measurement of angle A is 40
BC is 5
sin 40 = 5/AB
tan 40 = 5/AC
To find the measures of the other sides of triangle ABC, we can use trigonometric ratios. Since angle C is a right angle, we can use the Pythagorean theorem to find the length of side AB.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the length of side AB as x and the length of side AC as 5 (given). We can use the Pythagorean theorem to find x:
x^2 = (AC)^2 + (BC)^2
x^2 = 5^2 + 5^2
x^2 = 25 + 25
x^2 = 50
x ≈ √50
x ≈ 7.07
So, the length of side AB is approximately 7.07.
To find the length of side BC, we can use trigonometric ratios. Since angle A is given as 40 degrees, we can use the sine ratio.
The sine ratio states that the ratio of the length of the side opposite an angle to the length of the hypotenuse is equal to the sine of that angle.
sin(A) = BC / AC
sin(40) = BC / 5
To find BC, we can rearrange the equation:
BC = sin(40) * 5
Using a calculator, we find:
BC ≈ 0.643 * 5
BC ≈ 3.21
So, the length of side BC is approximately 3.21.
Therefore, the measures of the other sides to the nearest whole number are:
AB ≈ 7
BC ≈ 3