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The picture shows a triangular island: a right triangle is shown with an acute angle equal to 45 degrees. the length of the side of the triangle opposite to the acute angle is a. the length of the side of the triangle adjacent to the acute angle is b. the length of the hypotenuse is c. which expression shows the value of c?

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Final answer:

The expression to find the hypotenuse c in a right-angled triangle where the lengths of the other two sides a and b are known is c = √(a² + b²) according to the Pythagorean theorem.

Step-by-step explanation:

To find the value of the hypotenuse c in a right triangle where the sides opposite and adjacent to the acute angle are known, we use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). Specifically, the relationship is given by the equation a² + b² = c².

In the case of a right triangle with a 45-degree angle, if one side is a and the other side is b, both of which are the legs of the triangle, and given that this triangle conforms to the characteristics of a right triangle, we can find c by rearranging the theorem to solve for the hypotenuse:

c = √(a² + b²)

This expression allows us to calculate the length of the hypotenuse if we know the lengths of the other two sides. It's also useful to remember that in a right triangle with a 45-degree angle, the lengths of the two legs are equal if the angles opposite them are also 45 degrees (a = b). However, since the question specifies that a and b are different, we will not assume they are equal here.

User Colette
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Final answer:

The value of the hypotenuse c in a right triangle with sides a and b can be calculated using the Pythagorean theorem, expressed as c = √(a² + b²).

Step-by-step explanation:

To find the value of the hypotenuse c in a right triangle where one angle is 45 degrees and the lengths of the other two sides are a and b, you can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c). Therefore, the expression for c is given by:

c = √(a² + b²)

This formula allows you to calculate the length of the hypotenuse given the lengths of the other two sides a and b.

The complete question is: What are right triangle trigonometry problems?

User GleasonK
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