John runs to the market and comes back in 15 minutes. His speed on the way to the market is 5m/s and his speed on the way back i
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Answer:
The tree is 17.5 ft tall
Step-by-step explanation:
We can use proportions to solve this.
Notice that Emily (5 feet tall) and her shadow (8 feet long) constitute the two legs of a right angle triangle (see attached image).
The nearby tree (unknown height H), will also cast a shadow (28 ft long) with the same inclination as Emily does due to the unique position of the sun relative to them.
Then we can use the proportion associated with the sides of similar triangles:
Then, we can solve for H in the equation:
Answer:
Step-by-step explanation:
tan is defined as:
sin is defined as:
cos is defined as:
We can also define tan as:
because plugging in the definitions of sin and cos in we get:
which you'll notice is the original definition of tan(x)
So using this definition of tan(x) we can use the givens sin(x) and cos(x) to find tan(x)
plugging in sin(x) and cos(x) we get:
We usually don't like square roots in the denominator, and from here we want to rationalize the denominator which we do by removing the square root from the denominator.
We can do this by multiplying the fraction by: which doesn't change the value of the fraction since it simplifies to 1, but it gets rid of the square root in the denominator