If the hypotenuse of a right triangle is 10 units and angle B is 70 degrees determine angle A and the other sides of the triangle.

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hala718's profile pic

Posted on

Given the triangle ABC such that:

B = 70 degrees.

Then The other angles are:

A = 90 degrees.

C = 20 degrees.

Then the hypotenuse is BC = 10 units.

Now we will calculate the length of the legs.

==> AC = BC*cos B = 10*cos70 = 10*0.3420 = 3.42 units

==> AB = BC*cos C = 10*cos20 = 10*0.9397 = 9.367 units.

Then the angles of the triangle are:

A = 90 degrees

B = 70 degrees.

C = 20 degrees.

The length of the sides are:

AB = 9.367 units.

BC = 10 units.

AC = 3.42 units.

justaguide's profile pic

Posted on

We have a right angled triangle and one of the sides given as 70 degrees. Now the second side is 180 - 90 - 70 = 20 degrees.

Also, the hypotenuse is 10. Let the other sides be a and b.

So cos 70 = a / 10 =.3420

a = .3420*10 = 3.420

cos 20 = b/ 10 = .9396

b = 0.9396*10 = 9.396

Therefore the sides of the triangle are 10, 3.42 and 9.396. The angles of the triangle are 90, 70 and 20 degrees.

giorgiana1976's profile pic

Posted on

Let's suppose that the right angle is A = 90 degrees. The hypotenuse is opposite side to the right angle.

That means that B+C = 70 + C = 90

C = 90 - 70

C = 20 and B = 70

To determine the lengths of the other cathetus, we'll apply the Pythagorean theorem and the sine function.

The sine function is a ratio between the opposite cathetus and the hypothenuse. We'll note the cathetus as x and y.

sin B = x/10

sin 70 = x/10

x = 10*sin 70

x = 10*0.93

x = 9.4 units

We'll apply Pythagorean theorem in a right angle triangle:

10^2 = x^2 + y^2

100 = 88.36 + y^2

y^2 = 100 - 88.36

y^2 = 11.64

y = 3.4 units

We'll keep only the positive value for y, since it is the length of the cathetus of the right angle triangle and it cannot be negative.

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