$\bf \cfrac{sin(t)+tan(t)}{tan(t)}\impliedby \textit{distributing the denominator}
\\\\\\
\cfrac{sin(t)}{tan(t)}+\cfrac{tan(t)}{tan(t)}\implies \cfrac{sin(t)}{\frac{sin(t)}{cos(t)}}+1\implies 
\cfrac{\frac{sin(t)}{1}}{\frac{sin(t)}{cos(t)}}+1
\\\\\\
\cfrac{sin(t)}{1}\cdot \cfrac{cos(t)}{sin(t)}+1\implies cos(t)+1$

8 0

3 years ago

Use the information giving in the figure to find the length FH. If applicable, round your answer to the nearest whole number.

Dimas [21]

9514 1404 393

Answer:

FH = 16

Step-by-step explanation:

ΔGHE is a 5-12-13 triangle.

ΔEHF is a 3-4-5 triangle with a scale factor of 4, so side FH is 4·4 = 16 units.

_____

(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17) are all commonly used Pythagorean triples. The first two on the list are used in these triangles.

If you like, you can work out the numbers using the Pythagorean theorem, which tells you the square of the hypotenuse is equal to the sum of the squares of the other two sides.

For ΔEHG, that is ...

GE² = EH² + HG²

13² = EH² + 5²

EH² = 13² -5² = 169 -25 = 144

And for ΔEHF, ...

FE² = EH² +HF²

20² = 144 + HF²

400 -144 = HF² = 256

HF = √256 = 16

The length of side FH is 16 units.

5 0

2 years ago