If a right triangle has one angle of 53 degrees and one side with a length of 7.5 N?

Question

How do you find the lengths of all the sides and the measure of all the angles? do i have to use the formula of sine, cosine and tangent? if so,can anyone give me the formula using sine, cosine and tangent. Thanks a bunch

Answer 1

The angles are easy. The three angles of every triangle add up to 180 degrees everytime. So if one is 90 (defining characteristic of a right triangle), and another is 53, then the third angle is 37 degrees. With the sides, we could find the other two, but we need to know which side it is. Is 7.5 the hypotenuse, the height, or the base? Which one it is will tell you which formula to use. For example, if it's the hypotenuse (the one opposite the 90 degree angle), then you'd want to use sin53=x/7.5 to find the side opposite the 53 degree angle. If it's a side, then use sin * (whichever angle opposes the side in question)=7.5 /x to find the hypotenuse. Make sense?

Answer 2

Given a right triangle, you now that it has a 90 degree angle. You also know the sum of all the angles should equal 180. Given two angles, you could find the third.

let a = the angle of the 3rd angle
90 + 53 + a = 180

solving for a:
143 + a = 180 (adding 90+53)
a = 180 - 143 (subtracting 143 from each side)
a = 37

therefore the angles of the triangle is: 90, 53, and 37

To solve for the length, of each side, you could use Pythagorean theorem. Pythagorean theorem: given a right triangle with one side of length "a", another side of length "b", and the hypotenuse (the side directly accross from the right triangle) of length "c", a^2 + b^2 = c^2

you also know, given an angle that is not a right angle, "theta", and a length a directly accross from the angle is "a", and the length of the side adjacent to the angle, that is not the hypotnuse is "b", and "c" is the hypotnuse
sin(theta) = a/c
cos(theta) = b/c
tan(theta) = a/b

In your problem, you did not state the position of the side so I can't give you a proper answer.

Answer 3

Soh-cah-toa!

Sine x = O/H

Cosine x = A/H

Tangent x = O/A

Where x is your angle and O is the length of the side directly opposite your angle, H is the length of the hypotaneuse, and A is the length of the side adjancent to your angle.

So for your problem, you need to know which side (opposite, adjacent, or hypotaneuse) that length is. Try probably gave you a picture of the triangle?

Answer 4

basically, use sine if you want to get the measure of a siide opposite from that angle, cosine for the adjacent sides. consequently, you can use sine and cosine to get the angles using the measure of the sides.
sinex = opposite side / hypothenuse
cosinex = adjacent side / hypothenuse
tangentx = opposite / adjacent side
where x is an angle.
use sohcahtoa - Sine is Opposite over Hypothenuse, Cosine for the Adjacent over Hypothenuse, and Tangent is Opposite over Adjacent. always check with a calculator to see if your calculations are correct.

Answer 5

A scalene triangle. Scalene triangles are unusual in that the are defined through what they don't look to be. maximum triangles drawn at random will be scalene. the interior angles of a scalene triangle are continuously all diverse. The talk of it is likewise actual - If all 3 angles are diverse, then the triangle is scalene, and all the perimeters are diverse lengths.

Answer 6

Please learn this. You really may need to do this later in life and that's why you should do your own homework instead of copying and pasting the answer.