QuestionFind the missing side of a right triangle with sides 3.9 and 11. What is the length? Options: A) 6.5 B) 3.4 C) 11.9 D) 10.3

Studdy Solution

STEP 1

Assumptions1. The triangle is a right triangle. The given sides are3.9 and113. We are looking for the length of the missing side, which could be either the hypotenuse or one of the legs

STEP 2

We will use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as $a^2 + b^2 = c^2$ where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

STEP 3

First, we need to determine if the missing side is the hypotenuse or one of the legs. If11 is the hypotenuse, then the missing side is a leg and we should subtract the square of3.9 from the square of11. If3.9 is the hypotenuse, then the missing side is a leg and we should subtract the square of11 from the square of3.9.Since11 is greater than3.9, we assume11 is the hypotenuse. So, we calculate the square of the missing side as $Missing\, side^2 = c^2 - a^2$

STEP 4

Substitute the given values into the equation $Missing\, side^2 =11^2 -3.9^2$

STEP 5

Calculate the square of the missing side $Missing\, side^2 =121 -15.21$

STEP 6

Subtract to find the square of the missing side $Missing\, side^2 =105.79$

STEP 7

To find the length of the missing side, we take the square root of the result $Missing\, side = \sqrt{105.79}$

STEP 8

Calculate the length of the missing side $Missing\, side =10.3$ So, the length of the missing side of the triangle is10.3. The correct answer is D)10.3.

Was this helpful?

QuestionFind the missing side of a right triangle with sides 3.9 and 11. What is the length? Options: A) 6.5 B) 3.4 C) 11.9 D) 10.3

Studdy Solution

STEP 1

Assumptions1. The triangle is a right triangle. The given sides are3.9 and113. We are looking for the length of the missing side, which could be either the hypotenuse or one of the legs

STEP 2

STEP 3

STEP 4

Substitute the given values into the equation $Missing\, side^2 =11^2 -3.9^2$

STEP 5

Calculate the square of the missing side $Missing\, side^2 =121 -15.21$

STEP 6

Subtract to find the square of the missing side $Missing\, side^2 =105.79$

STEP 7

To find the length of the missing side, we take the square root of the result $Missing\, side = \sqrt{105.79}$

STEP 8

Calculate the length of the missing side $Missing\, side =10.3$ So, the length of the missing side of the triangle is10.3. The correct answer is D)10.3.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the missing side of a right triangle with sides 3.9 and 11. What is the length? Options: A) 6.5 B) 3.4 C) 11.9 D) 10.3

Studdy Solution

STEP 1

Assumptions1. The triangle is a right triangle. The given sides are3.9 and113. We are looking for the length of the missing side, which could be either the hypotenuse or one of the legs

STEP 2

STEP 3

STEP 4

Substitute the given values into the equationMissing side2=112−3.92Missing\, side^2 =11^2 -3.9^2Missingside2=112−3.92

STEP 5

Calculate the square of the missing sideMissing side2=121−15.21Missing\, side^2 =121 -15.21Missingside2=121−15.21

STEP 6

Subtract to find the square of the missing sideMissing side2=105.79Missing\, side^2 =105.79Missingside2=105.79

STEP 7

To find the length of the missing side, we take the square root of the resultMissing side=105.79Missing\, side = \sqrt{105.79}Missingside=105.79​

STEP 8

Calculate the length of the missing sideMissing side=10.3Missing\, side =10.3Missingside=10.3So, the length of the missing side of the triangle is10.3. The correct answer is D)10.3.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Substitute the given values into the equation $Missing\, side^2 =11^2 -3.9^2$

Calculate the square of the missing side $Missing\, side^2 =121 -15.21$

Subtract to find the square of the missing side $Missing\, side^2 =105.79$

To find the length of the missing side, we take the square root of the result $Missing\, side = \sqrt{105.79}$

Calculate the length of the missing side $Missing\, side =10.3$ So, the length of the missing side of the triangle is10.3. The correct answer is D)10.3.