Difference between revisions of "Find the Area of an Isosceles Triangle"
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#*The other short side is the height, ''h''. | #*The other short side is the height, ''h''. | ||
#*The hypotenuse of the right triangle is one of the two equal sides of the isosceles. Let's call it ''s''. | #*The hypotenuse of the right triangle is one of the two equal sides of the isosceles. Let's call it ''s''. | ||
| − | #[[Use | + | #[[Use the Pythagorean Theorem|Set up the Pythagorean Theorem]]. Any time you know two sides of a right triangle and want to find the third, you can use the Pythagorean theorem: (side 1)<sup>2</sup> + (side 2)<sup>2</sup> = (hypotenuse)<sup>2</sup> Substitute the variables we're using for this problem to get <math>(\frac{b}{2})^2 + h^2 = s^2</math>. |
#*You probably learned the Pythagorean Theorem as <math>a^2 + b^2 = c^2</math>. Writing it as "sides" and "hypotenuse" prevents confusion with your triangle's variables. | #*You probably learned the Pythagorean Theorem as <math>a^2 + b^2 = c^2</math>. Writing it as "sides" and "hypotenuse" prevents confusion with your triangle's variables. | ||
#Solve for ''h''. Remember, the area formula uses ''b'' and ''h'', but you don't know the value of ''h'' yet. Rearrange the formula to solve for ''h'': | #Solve for ''h''. Remember, the area formula uses ''b'' and ''h'', but you don't know the value of ''h'' yet. Rearrange the formula to solve for ''h'': | ||
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===Using Trigonometry=== | ===Using Trigonometry=== | ||
| − | #Start with a side and an angle. If you know some [[Use | + | #Start with a side and an angle. If you know some [[Use Right Angled Trigonometry|trigonometry]], you can find the area of an isosceles triangle even if you don't know the length of one of its side. Here's an example problem where you only know the following:<ref name="rf2" /> |
#*The length ''s'' of the two equal sides is 10 cm. | #*The length ''s'' of the two equal sides is 10 cm. | ||
#*The angle θ between the two equal sides is 120 degrees. | #*The angle θ between the two equal sides is 120 degrees. | ||
