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.

Expert Answers

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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.

Approved by eNotes Editorial Team
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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.

Approved by eNotes Editorial Team

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