Answer:
x = 8.0
Step-by-step explanation:
sin theta = opposite/ hypotenuse
sin 53 = x/10
Multiply by 10 on each side
10 sin 53= x
7.9863551 =x
Rounding to the nearest tenth
8.0 =x
Answer:
Step-by-step explanation:
It can be convenient to compute the length of the hypotenuse of this triangle (AC). The Pythagorean theorem tells you ...
AC^2 = AB^2 + CB^2
AC^2 = 4^2 + 3^2 = 16 + 9 = 25
AC = √25 = 5
The altitude divides ∆ABC into similar triangles ∆AHB and ∆BHC. The scale factor for ∆AHB is ...
scale factor ∆ABC to ∆AHB = AB/AC = 4/5 = 0.8
And the scale factor to ∆BHC is ...
scale factor ∆ABC to ∆BHC = BC/AC = 3/5 = 0.6
Then the side AH is 0.8·AB = 0.8·4 = 3.2
And the side CH is 0.6·BC = 0.6·3 = 1.8
These two side lengths should add to the length AC = 5, and they do.
The remaining side BH can be found from either scale factor:
BH = AB·0.6 = BC·0.8 = 4·0.6 = 3·0.8 = 2.4
_____
The sides of interest are ...
AH = 3.2
CH = 1.8
BH = 2.4
If he travels 5/2 miles in 15 mins, then in 1 min he will travel 5/2 ÷ 15 = 1/6 miles and it will take him 15 ÷ 5/2 = 6 mins to travel 1 mile.
A. x = -2 and y = -5
check:
x^2 - 9 = 0
B. x = 0 and y = -6
check:
x^2 - 6 = 0
C. x1 = 3, x2 = 5
check:
(x - 3)(x - 5) = 0
D. x1 = 0, x2 = 4
check:
x(x - 4) = 0