Part A)<span>In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 11 in.?
we know that
</span>cos 45°=√2/2
[he length of the hypotenuse]=11/cos 45-----------> 11/(√2/2)----> (11*2)/√2
=22/√2-------> 11√2 in
the answer Part A) is 11√2 in
Part B) <span>What is the exact value of sin 45° ?
</span>
we know that
sin 45°=11/(11√2)-------> 1/√2---------> (1/√2)*(√2/√2)-----> √2/2
the answer part b) is √2/2
Part C)
<span>What is the area of a regular hexagon with a side length of 4 m?
we know that
</span>In case of a regular hexagon <span> each of the six triangles that are formed by connecting its center with all six vertices is an equilateral triangle with a side equaled to 4 m.
The area of this hexagon is six times greater than the area of such a triangle
</span>
In an equilateral triangle with a side d<span>
the altitude </span>h can be calculate from the Pythagorean Theorem as
h²=d²−(d/2)²=(3/4)d²
<span>Therefore,
</span><span>h=d<span>√3/2
</span></span><span>Area of such a triangle is
</span>A=d*h/2------------> d²*√3/4
From this the area of the regular hexagon with a side d<span> is
</span>S=6*A----------> d²3√3/2
for d=4 m
S=4²3√3/2------> 24√3 m²------------> 41.57 m²
the answer Part C) is 41.57 m²
Part D) <span>In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
</span>[he length of the hypotenuse]=5/sin 30--------> 5/(1/2)---------> 10 cm
the answer part D) is 10 cm
in not sure if it would be correct but i think it would be c because the lines would eventually cross through eachother
Step-by-step explanation:
Answer:
125
Step-by-step explanation:
( 3x - 70 ) is exterior angle.
60 and x are interior angles.
Formula : -
Exterior angle of a triangle
= Sum of two interior angles in a triangle
3x - 70 = x + 60
3x - x = 60 + 70
2x = 130
x = 130 / 2
x = 65
m∠LKM = 3x - 70
= 3 ( 65 ) - 70
= 195 - 70
m∠LKM = 125
We can solve the puzzle by simplifying the conditions in the table below:
Husband Wife Place Visited Means
Eugene Chloe Stake Out not Limousine
not David, then Flavian Belinda Rainbo IV then Limousine
then David Andrea then Water World fun park Taxi
Therefore, from the given conditions, David and Andrea spent their evening at Water World fun park and they got there by taxi.
