We are given the triangle
△ABC, with m∠A=60° and m∠C=45°, and AB=8.
To start, we will calculate all angles and sides.
Finding angle B:
The total of all angles in a triangle equals 180.
m∠A + m∠B + m∠C = 180.
Substituting the known values,
60° + m∠B + 45° = 180.
This gives us m∠B = 75°.
Calculating BC:
Using the law of sines,
We can substitute in the values.
Finding AC:
Now we'll input the values.
Calculating Perimeter:
We substitute values here as well.
Calculating Area:
Using the area formula,
we can then insert values.
...............Answer
The vertex of the graph for the function g(x) = (x- 3)^2 + 9 is located 3 units to the right and 9 units upwards compared to the vertex of the function f(x) = x^2.
Answer:
C. The hypotenuse measures twice the distance of the shorter leg.
B. The longer leg is √3 times the length of the shorter leg.
Step-by-step explanation:
A 30-60-90 triangle is considered a right triangle. Triangles containing a right angle are classified as right triangles. Only one right angle can exist in such a triangle. The representation of this case is illustrated below. Let’s clarify why the proposed statements are valid:
The hypotenuse of a right triangle is always opposite to the right angle. If we designate 
as the shorter leg, the sine law affirms that the hypotenuse is:
This indicates that the hypotenuse is double the length of the shorter leg
The longer leg, which we can call 
, can be determined with the Pythagorean Theorem:
Thus, it is accurate that the longer leg is √3 times longer than the shorter leg.
ABCD forms a rhombus with adjacent sides that are not perpendicular.
Simple interest can be calculated using the formula:
S.I = P*T*R
Where S.I represents the simple interest to determine
P signifies the principal amount
T represents the time in years
R is the annual interest rate
In this instance:
The principal (P) is $400
The duration is 6 months, equivalent to 1/2 year
The annual interest rate is set at 6.8%, which is 6.8/100 or 0.068
Calculating Simple Interest gives us:
Simple Interest = P*T*R
Simple Interest = 400*1/2*0.068 = 200 *0.068
Simple Interest = $13.6
At the end of six months, Miguel must pay Julio $13.6 in interest.
