Trigonometry?

Question

I have a triangle that contains 1 right angle. What is the formula to work out the length of 1 unknown side and the angle of the other two sides.

If it helps the dimensions of two sides are 12.5cm and 95cm. It is 12.5cm tall and 95cm down a slanted edge. The base of the triangle is unkown but the base to height is 90 degree angle. What is the angle from base to the 95 cm slanted edge?

Answer 1

From the information you presented, the 12.5 cm is the opposite and 95 cm side is the hypothenuse. The formula for sin x is opposite over hypothenuse.

If x is the angle opposite of the 12.5 cm side, then sin x = 12.5/95. Find sin x by keying in 12.5/95 sin^-1 (or sin^-1 12.5/95 depending on your calculator) in your calculator. In this case, you should get approximately 7.56 degrees (make sure you set your calculator to degree mode and not radian mode).

Subtract 90 and this 7.56 from 180 (sum of the degrees of angles in a triangle) to get 82.44 degrees for the 3rd angle.

Since you know the 7.56 angle, you can find the cos 7.56 with 95 as the hypothenuse. cos x is equal to the length of the side adjacent to the angle over hypothenuse. Check this equation out (if a is the length of the adjacent side):

cos 7.56 = a / 95
95 (cos 7.56) = a
a = 94.17

Therefore, the other angles are 7.56 degrees (opposite the 12.5-cm side) and 82.44 (between the 12.5-cm and 95-cm side) while the unknown side is 94.17 cm.

Alternatively, you can easily find the length of the 3rd side using the pythagorean theorem:

a^2 + b^2 = c^2
The 95 cm is your c (hypothenuse) while you can substitute 12.5 to either a or b leaving the other blank. Let us say 12.5 is a. You have:

12.5^2 + b^2 = 95^2

solving the equation, you get:
156.25 + b^2 = 9025
b^2 = 8868.75
b = 94.17 cm

As we can see, the length of the unknown side is 94.17 cm in length, identical to the 1st approach.

Answer 2

If ABC is a right angled triangle with sides AB and BC, and AC is the hyptenuse (the slanting side), the relationship is:

AB^2 + BC ^2 = AC^2

So, if we know two of them, we can calculate the third. In the present case, we know BC and AC and we need AB the base.

AB^2 = AC^2 - BC^2 = 95^2 - 12.5^2 = 9025 - 156.25 = 8868.75

So, AB = sqrt.8868.75 = 94.17 cm

Angle subtended by base to the hypotenuse (slanted edge) is given by base/slanted edge = cos theta where theta is the angle.

94.17/95 = 0.9913

And theta the angle = cos^-1 0.9913 = 7.56 degrees. The other angle will be 90 - 7.56 = 82.44 and between the height and the slanted edge. That is because the total of angles in a triangle is 180 degrees and we already have a right angle i.e. 90 degrees between the height and the base.

Answer 3

Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.

Answer 4

Break out the protractor. Just remember that all the angles of the triangle add up to 360, but, you've already eliminated 90 degrees, so that leaves you with 270 degrees to play with. That's the best I can do, I haven't taken any math classes in like 4 years so, good luck...

Answer 5

the base is 94.174the angle formed by the hypotenuse and the vertical line is 82.4 and the angle made by the base and the vertical line is 7.56

u simply use the pythagorean theorem and the trigonometric functions

Answer 6

(sinA)/a=(sinB)/b=(sinC)/c

so
sinA/a=sinB/b

A=90 degrees
a=95 cm
B=?
b=12.5

sin90/95=sinX/12.5
X=7.561 degrees