Question Find the lengths of the shorter sides of a 45°-45°-90° triangle with longest side 8. Exact answer.

Studdy Solution

STEP 1

Assumptions1. The triangle is a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle. . The longest side (hypotenuse) is8.
3. We are looking for the lengths of the other two sides.

STEP 2

In a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, the sides opposite the $45^{\circ}$ angles are equal in length. Let's denote this length as $a$ . The side opposite the $90^{\circ}$ angle (the hypotenuse) is $\sqrt{2}$ times the length of each of the other sides. We can write this relationship as $Hypotenuse = a \cdot \sqrt{2}$

STEP 3

Now, plug in the given value for the hypotenuse to find the length of the other sides.
$8 = a \cdot \sqrt{2}$

STEP 4

To solve for $a$ , divide both sides of the equation by $\sqrt{2}$ .
$a = \frac{8}{\sqrt{2}}$

STEP 5

Rationalize the denominator by multiplying the numerator and the denominator by $\sqrt{2}$ .
$a = \frac{8 \cdot \sqrt{2}}{2}$

STEP 6

implify the right side of the equation to find the length of the other sides.
$a =4\sqrt{2}$ Both shorter sides of the triangle are $4\sqrt{2}$ units long.

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Question Find the lengths of the shorter sides of a 45°-45°-90° triangle with longest side 8. Exact answer.

Studdy Solution

STEP 1

Assumptions1. The triangle is a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle. . The longest side (hypotenuse) is8.
3. We are looking for the lengths of the other two sides.

STEP 2

STEP 3

Now, plug in the given value for the hypotenuse to find the length of the other sides.
$8 = a \cdot \sqrt{2}$

STEP 4

To solve for $a$ , divide both sides of the equation by $\sqrt{2}$ .
$a = \frac{8}{\sqrt{2}}$

STEP 5

Rationalize the denominator by multiplying the numerator and the denominator by $\sqrt{2}$ .
$a = \frac{8 \cdot \sqrt{2}}{2}$

STEP 6

implify the right side of the equation to find the length of the other sides.
$a =4\sqrt{2}$ Both shorter sides of the triangle are $4\sqrt{2}$ units long.

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Question Find the lengths of the shorter sides of a 45°-45°-90° triangle with longest side 8. Exact answer.

Studdy Solution

STEP 1

Assumptions1. The triangle is a 45∘−45∘−90∘45^{\circ}-45^{\circ}-90^{\circ}45∘−45∘−90∘ triangle. . The longest side (hypotenuse) is8.3. We are looking for the lengths of the other two sides.

STEP 2

STEP 3

Now, plug in the given value for the hypotenuse to find the length of the other sides.8=a⋅28 = a \cdot \sqrt{2}8=a⋅2​

STEP 4

To solve for aaa, divide both sides of the equation by 2\sqrt{2}2​.a=82a = \frac{8}{\sqrt{2}}a=2​8​

STEP 5

Rationalize the denominator by multiplying the numerator and the denominator by 2\sqrt{2}2​.a=8⋅22a = \frac{8 \cdot \sqrt{2}}{2}a=28⋅2​​

STEP 6

implify the right side of the equation to find the length of the other sides.a=42a =4\sqrt{2}a=42​Both shorter sides of the triangle are 424\sqrt{2}42​ units long.

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Assumptions1. The triangle is a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle. . The longest side (hypotenuse) is8.
3. We are looking for the lengths of the other two sides.

Now, plug in the given value for the hypotenuse to find the length of the other sides.
$8 = a \cdot \sqrt{2}$

To solve for $a$ , divide both sides of the equation by $\sqrt{2}$ .
$a = \frac{8}{\sqrt{2}}$

Rationalize the denominator by multiplying the numerator and the denominator by $\sqrt{2}$ .
$a = \frac{8 \cdot \sqrt{2}}{2}$

implify the right side of the equation to find the length of the other sides.
$a =4\sqrt{2}$ Both shorter sides of the triangle are $4\sqrt{2}$ units long.