Question

(3, 4) find the value for cosine? *
3/5
4/5
4/3

find a , when b = 20 and c=29 *
19
17
15
none of the above

Explanation:

Step1: For the first problem

Given the point (3, 4), we first find the hypotenuse $r$ using the Pythagorean theorem $r=\sqrt{x^{2}+y^{2}}$, where $x = 3$ and $y = 4$. So $r=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5$. The cosine of the angle in standard - position is given by $\cos\theta=\frac{x}{r}$. Substituting $x = 3$ and $r = 5$, we get $\cos\theta=\frac{3}{5}$.

Step2: For the second problem

Using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, we want to find $a$. Rearranging for $a$, we have $a=\sqrt{c^{2}-b^{2}}$. Given $b = 20$ and $c = 29$, then $a=\sqrt{29^{2}-20^{2}}=\sqrt{(29 + 20)(29 - 20)}=\sqrt{49\times9}=\sqrt{441}=21$. Since 21 is not among the options, the answer is none of the above.

Answer:

A. 3/5
D. none of the above