Answer:
49°
Step-by-step explanation:
We are given:
m∠1 = 50°
m∠2 = 48°
Since m║n and s bisects ∠ABC (this means that line s cuts the angle in half) and as you can see, the line extends, bisecting the angle across it.
We have this theorem about corresponding angles, when a line transverses across two parallel lines. ∠ABC corresponds to the angle that ∠3 is a part of. Look at the picture to see what I am referring to. The red lines show the corresponding angles.
m∠1 and m∠2 summed up would be equal to the measure of ∠ABC.
m∠1 = 50°
m∠2 = 48°
m∠1 + m∠2 = ∠ABC
50° + 48° = ∠ABC
98° = ∠ABC
This means that the corresponding angle is also equal to 98°.
Now since the s bisects the corresponding angle forming ∠3, we just divide the measure of the angle by 2 and we have your answer:
m∠3 = 98°/2
m∠3 = 49°
Answer:
D
Step-by-step explanation:
side HG is 3
side FG is 5 hypotenuse
sin F = 3/5 = opposite/hypotenuse
cos G is adjacent/hypotenuse
adjacent side is HG which = 3
hypotenuse is 5
First let's find the angles a and b.
We have then:
sin a = 4/5
a = Asin (4/5)
a = 53.13 degrees.
cos b = 5/13
b = Acos5 / 13
b = 67.38 degrees.
We now calculate cos (a + b). To do this, we replace the previously found values:
cos ((53.13) + (67.38)) = - 0.507688738
Answer:
-0.507688738
Note: there is another way to solve the problem using trigonometric identities.
Answer:
5.20 to the nearest hundredth.
Step-by-step explanation:
The altitude line bisects the base of the triangle to form 2 right angled triangles with hypotenuse = 6 and the base = 3.
So, by the Pythagoras theorem the altitude is calculated as follows:
6^2 = 3^2 + x^2
x^2 = 36 - 9 = 27
x = √27
= 5.20 to the nearest hundredth.
The went 25.6 miles on one gallon of gas. Hope this helps!