The measure of one of the small angles of a right triangle is 18 less than twice the measure of the other small angle. find the measure of both angles. use integers only

36° and 54°

Step-by-step explanation:

We are given that one of the small angles of a right angled triangle is 18 less than twice the measure of the other small angle.

We are to find the measure of both angles.

Assuming to be the other small angle, 8 less than twice the measure of the other small angle = .

Summing all three angles up ti get:

x = 36°

So other angle will be 54°.

36° and 54°

Step-by-step explanation:

let x be one of the smaller angles, then the other smaller angle is 2x - 18 ( 18 less than twice the other )

Since it is a right triangle then the sum of the 2 smaller angles equals 90, so

x + 2x - 18 = 90

3x - 18 = 90 ( add 18 to both sides )

3x = 108 ( divide both sides by 3 )

x = 36

One angle = 36°

the other angle = (2 × 36) - 18 = 72 = 18 = 54°

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).