The hypotenuse of a right triangle is 1000, and one of its angles is 87 degrees.

Question

(a) Find the legs and the area of the triangle, correct to three decimal places.

(b) Write a formula for the area of a right triangle in which h is the length of the hypotenuse and A is the size of one of the acute angle.

(c) Apply your formula (b) to redo part  (a) Did you get the same answer? Explain.

Answer 1

 

Since this is a right triangle, one of the 3 angles is 90 degrees, by definition.

A second angle is 87 degrees (given)

The third angle is 3 degrees, because the sum of all angles in a right triangle is 180 degrees

 

Note that capital letters denotes angles, and the lower case letters denotes the sides

The lower-case side is always opposite the upper case angle.

 

Let angle A be the 87 degree angle, and angle B be the 3 degree angle

 

the sine of an acute angle of a right triangle is ... sine = opposite/hypotenuse

 

   Sine A = opposite/hypotenuse

 

   Sine 87 = a / 1000

 

   NOTE:  make sure calculator is in degree mode

 

   a = 1000 * (sine 87)

   a = 998.63

 

   Sine B = opposite/hypotenuse

 

   Sine 3 = b / 1000

 

   b = 1000 * sine 3

   b = 52.34

 

so lengths of the other 2 sides (legs) of the triangle are 52,34 and 998.63