How to find the 3rd side of a right triangle

Asked by admin @ in Mathematics viewed by 460 People

Two sides of a right triangle are equal to 3m and 4m. Find the length of the third side. (Two cases)If the two given sides are both legs, then the length of the third side is _ m. If the two given sides are a leg and the hypotenuse, then the length of the third side is _ m.

Answered by admin @


Case 1: The length of the third side (hypotenuse) is 5m.


My Reasoning/Work:
We use the Pythagorean theorem (a^2+b^2=c^2), the two legs in the Pythagorean theorem are "a" and "b" and the third leg/the hypotenuse, is "c". 3^2+4^2=c^2
Then, we find the squares of 3 and 4, and then add them up. 9+16=25
Now that we know that the square of the third side is 25m, we now find the square root of 25. \sqrt{25}=5
The hypotenuse is 5m.


Case 2: The length of the third side (the leg) is \sqrt{7} m.

My Reasoning/Work:
Again, we'll use the Pythagorean theorem. a^2+b^2=c^2
This time, instead of using the "b", we're using the "a" (leg) and the "c" (hypotenuse). Because the hypotenuse is the longest side in a right triangle, we get that "c" is equal to 4m. 3^2+b^2=4^2
And now we bring down the exponents. 9+b^2=16
We now subtract 9 from both sides to leave the "b^2" alone. 9-9+b^2=16-9 \\ b^2=7
Finally, we find the square root of 7 to get the answer. But if you use a calculator to find this, you'll get an annoying answer of decimals (2.645751311064591). So, to simplify this, the answer would be \sqrt{7}.

Similar Questions

How to find angle in right triangle with 3 sides

Asked by admin @ in Mathematics viewed by 371 persons

Explain how to find the measures of the angles in a right triangle, given the lengths of two sides.

How to find 2 unknown sides of a right triangle

Asked by admin @ in Mathematics viewed by 279 persons

Solve for the unknown side in the right triangle if b=24 and c=26 find a A.8 B.9 C.10 D.11

How to find sides and angles of a right triangle

Asked by admin @ in Mathematics viewed by 334 persons

Explain how to find the measures of the angles in a right triangle, given the lengths of two sides.

Find the length of side x in the right triangle

Asked by admin @ in Mathematics viewed by 372 persons

Which expression finds the length of side x in this right triangle?

How do you find one side of a right triangle

Asked by admin @ in Mathematics viewed by 292 persons

A right triangle has a hypotenuse length of 12, and one side length of 9. find the missing side length. do the side lengths form a pythagorean triple?

Find two sides of a right triangle given the hypotenuse

Asked by admin @ in Mathematics viewed by 326 persons

To solve for the hypotenuse of a right triangle, what information do you need? A. just the measure of one of the acute angles and the length of one side …

For the following right triangle find the side length x

Asked by admin @ in Mathematics viewed by 333 persons

For the following right triangle, find the side length X. round to nearest hundredth

The lengths of the sides of a right triangle are a and b, and the hypotenuse is c. find the area of the triangle. b = 2 in.; c = 6 in. a = sq. in.

Asked by maham237 @ in Mathematics viewed by 327 persons

What is the longest side of a right triangle called

Asked by admin @ in Mathematics viewed by 355 persons

What is the longest side of a right triangle called?

How to find sides of a 30 60 90 triangle

Asked by admin @ in Mathematics viewed by 307 persons

In a 30-60-90 triangle, the length of the side opposite the 30 degree angle is 8. Find the length of the side opposite the 60 degree angle.

How to find angles of a triangle with 2 sides

Asked by admin @ in Mathematics viewed by 348 persons

Explain how to find the measures of the angles in a right triangle, given the lengths of two sides.

How do you find the angles of a right triangle

Asked by admin @ in Mathematics viewed by 318 persons

Explain how to find the measures of the angles in a right triangle, given the lengths of two sides.

In a right triangle the longest side is

Asked by admin @ in Math viewed by 356 persons

In a right triangle the longest side is (a) perpendicular (b) hypotenuse (c) base (d) none​

Find the area of equilateral triangle with side 10cm

Asked by admin @ in Math viewed by 349 persons

Find the area of an equilateral triangle with side 10cm

A right triangle whose sides are 15cm and 20cm

Asked by admin @ in Math viewed by 339 persons

A right triangle whose sides are 15cm and 20cm, is made to revolve about its hypotenuse. find the volume of the double cone. (π = 3.14)

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

Asked by maham237 @ in Mathematics viewed by 18341 persons

All things algebra unit 7 polygons and quadrilaterals answer key

Asked by admin @ in Mathematics viewed by 8139 persons

Gina wilson all things algebra 2016 answer key unit 11

Asked by admin @ in Mathematics viewed by 5764 persons

Unit 1 geometry basics homework 4 angle addition postulate answers

Asked by maham237 @ in Mathematics viewed by 3930 persons

Unit 6 exponents and exponential functions homework 8 answer key

Asked by maham237 @ in Mathematics viewed by 3246 persons

The manager of a vacation resort believes that the ages

Asked by maham237 @ in Mathematics viewed by 2918 persons

What is 271 403 rounded to the nearest ten thousand

Asked by maham237 @ in Mathematics viewed by 2780 persons

Unit 1 geometry basics homework 3 angle relationships answer key

Asked by maham237 @ in Mathematics viewed by 2572 persons

Homework 2 parallelograms

Asked by maham237 @ in Mathematics viewed by 2494 persons

Why would a prism beat a sphere in a competition?

Asked by maham237 @ in Mathematics viewed by 2473 persons

John wants to send a letter to peter

Asked by maham237 @ in Mathematics viewed by 2458 persons

An artist sells a painting for 20.50 but uses 5.75

Asked by maham237 @ in Mathematics viewed by 2423 persons

Unit 4 congruent triangles homework 1 classifying triangles answer key

Asked by maham237 @ in Mathematics viewed by 2414 persons

Unit 4 congruent triangles homework 2 angles of triangles

Asked by maham237 @ in Mathematics viewed by 2068 persons

Compare the values of the 2s and 5s in 55220

Asked by maham237 @ in Mathematics viewed by 1791 persons