Question

Find the length of the missing side. If necessary, round to the nearest tenth. side A = 38 side b =b side  c = 34

Answer 1

The length of the missing side = side B = 17 (D) or 51(A)

Further explanation

Triangles are flat fields bounded by 3 intersecting sides and 3 angles

This side can be the same length or different.

If at an angle there is an angle of 90 degrees, this triangle is said to be a right angle

There is a hypotenuse in this triangle which is the sum of the two sides

$\large{\boxed{\bold{C^2=A^2+B^2}}$

where c = hypotenuse

a and b = side/leg

This formula is known as the Pythagorean theorem which states that:

the hypotenuse or the longest side in a right triangle equal to the sum of the squares of the other sides.

or

the sum of the squares of the length of the two sides equals the square of the length of the hypotenuse

While the angle formulas used are

• sin a = opposite / hypotenuse
• cos a = adjacent / hypotenuse
• tan a = opposite / adjacent

From the problem it is known that side A = 38 ,side b = b, side c = 34

There are 2 possible solutions to this problem because the image does not exist:

• 1. side A as the hypotenuse side (the longest side)

• 2. side B as hypotenuse side

Possible Solution no 1

A² = C²+B²(A=hypetenuse)

B² = A²-C²

B² = 38² - 34²

B² = 288

B = √288

B = 16.97, round to the nearest tenth ⇒ 17 (answer D)

Possible Solution no 2

B² = A²+C²(B=hypotenuse)

B² = 38² + 34²

B² = 2600

B = √2600

B = 50.99, round to the nearest tenth ⇒ 51 (answer A)

Learn more

the Sin rule

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trigonometric ratio

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the triangle angle

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Prove the converse of the Pythagorean Theorem

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Use Pythagoras' theorem

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Keywords: Pythagoras' theorem, the trigonometric, hypotenuse

Answer 2

A) 51, assuming this is a *right* triangle:

38^2+34^2 = 50.99^2, rounding 51!!