BarBhieLuhidn
Answered

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In a right triangle where a and b are the legs, and c is the hypotenuse, how long is the shorter leg if the longer leg and hypotenuse measures 15 cm and 17 cm respectively?​

Sagot :

SensAcheidn

Answer:

The shorter leg measures 8cm.

Step-by-step explanation:

We can solve the problem with the equation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

Lets assume that:

a = Longer leg

b = Shorter leg

We can now rewrite the equation to:

[tex] {15}^{2} + {b}^{2} = {17}^{2} [/tex]

Now let us solve:

[tex]225 + {b}^{2} = 289[/tex]

Transpose:

[tex] {b}^{2} = 289 - 225[/tex]

Solve:

[tex] {b}^{2} = 64[/tex]

Get the square root of both sides:

[tex] \sqrt{ {b}^{2} } = \sqrt{64} [/tex]

[tex]b = 8[/tex]

As stated earlier, we assumed that the shorter leg is b, so this means that the shorter leg is 7cm long. This is also true since 15cm is greater than 7cm.

Windyblossomidn

Answer:

8 cm

Step-by-step explanation:

You can use the Pythagorean Theorem to find the length of any side of a right triangle.

Formula: a² + b² = c² (where either a or b is the height and base of the triangle and c is the hypotenuse)

Given: longer leg = 15 cm

*You can choose between a and b. For the mean time, I will use a.

hypotenuse (c) = 17 cm

Substitute the given values in the formula and solve for b.

15² + b² = 17²

225 + b² = 289

b² = 289 - 225

b² = 64

*We need to get the square root of 64 because we are only looking for the value of b.

√b² = √64

b = 8

Therefore, the shorter leg is 8 cm.

Hope this helps :))

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