Answer:
(d) 71°
Step-by-step explanation:
The desired angle in the given isosceles triangle can be found a couple of ways. The Law of Cosines can be used, or the definition of the sine of an angle can be used.
<h3>Sine</h3>
Since the triangle is isosceles, the bisector of angle W is an altitude of the triangle. The hypotenuse and opposite side with respect to the divided angle are given, so we can use the sine relation.
sin(W/2) = Opposite/Hypotenuse
sin(W/2) = (35/2)/(30) = 7/12
Using the inverse sine function, we find ...
W/2 = arcsin(7/12) ≈ 35.685°
W = 2×36.684° = 71.37°
W ≈ 71°
<h3>Law of cosines</h3>
The law of cosines tells you ...
w² = u² +v² -2uv·cos(W)
Solving for W gives ...
W = arccos((u² +v² -w²)/(2uv))
W = arccos((30² +30² -35²)/(2·30·30)) = arccos(575/1800) ≈ 71.37°
W ≈ 71°
Number 1 is answer 1 Number 2 is answer 3 Number 3 is answer 4
Answer:
The length would be 30 and the width would be 20
Step-by-step explanation:
For the purpose of this, we'll set the width as x. We can then define the length as x + 10 since we know it is 10 ft longer than the width. Now we can use those along with the perimeter formula to solve for the width.
P = 2l + 2w
100 = 2(x + 10) + 2(x)
100 = 2x + 20 + 2x
100 = 4x + 20
80 = 4x
20 = x
Now since we know that the width is 20ft, we can add 10ft to it to get the length, which would be 30ft.
Answer:
The line crosses the y-axis at -2
Step-by-step explanation:
y = mx + b 'm is the slope and b is the y-intersect (the place where the graph comes across the y-axis.
y = mx + b; y = mx + b; b = -2.
W = 27
1 + 1/3L = w
1 + 1/3L = 27
1/3L = 26
L = 78
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