The measure of the angle between the hypotenuse and the <em>short</em> leg is 60° and we can conclude that the side with length 10 is not the <em>long</em> leg of the 30 - 60 - 90 <em>right</em> triangle. (Right choice: False)
<h3>Is the length of a known arm in a 30 - 60 - 90 right triangle the long arm?</h3>
In accordance with geometry, the length of the <em>long</em> arm of a 30 - 60 - 90 <em>right</em> triangle is √3 / 2 times the length of the hypotenuse, the length of the <em>short</em> arm is 1 / 2 times the length of the hypotenuse and the length of the <em>long</em> arm is √3 times the length of the arm.
Thus, the measure of the angle between the hypotenuse and the <em>short</em> leg is 60° and we can conclude that the side with length 10 is not the <em>long</em> leg of the 30 - 60 - 90 <em>right</em> triangle. (Right choice: False)
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Step-by-step explanation:
This is known as the triple tangent identity. Start with the fact that the three angles add up to 0.
(x − y) + (z − x) + (y − z) = 0
Subtract two terms to the other side and take the tangent:
x − y = -((z − x) + (y − z))
tan(x − y) = tan(-((z − x) + (y − z)))
Use reflection property:
tan(x − y) = -tan((z − x) + (y − z))
Now use angle sum identity:
tan(x − y) = -[tan(z − x) + tan(y − z)] / [1 − tan(z − x) tan(y − z)]
tan(x − y) = [tan(z − x) + tan(y − z)] / [tan(z − x) tan(y − z) − 1]
tan(x − y) [tan(z − x) tan(y − z) − 1] = tan(z − x) + tan(y − z)
tan(x − y) tan(z − x) tan(y − z) − tan(x − y) = tan(z − x) + tan(y − z)
tan(x − y) tan(z − x) tan(y − z) = tan(x − y) + tan(z − x) + tan(y − z)
<span>7 × (–3) × (–2)^2
= </span>-21 × 4
= - 84
Hope it helps
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Answer:
Step-by-step explanation:
