A right triangle has side lengths of 0.6 meter and 0.8 meter. What is the length of the hypotenuse? Round to the nearest tenth.
1 answer:
Use the Pythagorean theorem since you are working with a right triangle:
a^2+b^2=c^2a2+b2=c2
The legs are a and b and the hypotenuse is c. The hypotenuse is always opposite the 90° angle. Insert the appropriate values:
0.8^2+0.6^2=c^20.82+0.62=c2
Solve for c. Simplify the exponents (x^2=x*xx2=x∗x ):
0.64+0.36=c^20.64+0.36=c2
Add:
1=c^21=c2
Isolate c. Find the square root of both sides:
\begin{gathered}\sqrt{1}=\sqrt{c^2}\\\\\sqrt{1}=c\end{gathered}1=c21=c
Simplify \sqrt{1}1 . Any root of 1 is 1:
c=c= ±11 *
c=1,-1c=1,−1
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<h3>Given</h3>
- m∠REG = 78°
- mAR = 46°
- ER ≅ GA
<h3>Solution</h3>
- m∠GAR = 180° - m∠REG = 180° - 78° = 102° (supplementary angles sum to 180°)
- m∠TAR = 1/2mAR = 1/2(46°) = 23° (tangent chord angle is half the size of intercepted arc)
- m∠GAN = 180° - (m∠TAR + m∠GAR) = 180° - (23° + 102°) = 55° (straight angle is 180°)
- mAG = 2m∠GAN = 2(55°) = 110°
- mRE = mAG = 110° (as ER ≅ GA)
- mGE = 360° - (mAG + mAR + mRE) = 360° - (110° + 46° + 110°) = 94° (full circle is 360°)
