Question

A
44°
X
8 cm
5.5 cm
Give your answer correct to 1 decimal place.

Answer 1

Explanation:

First, we want to solve for the height using Pythagoras:

y^2+(5.5)^2=8^2

y=sqrt(33.75)

Using cosine, we see that cos=opposite/hypotenuse

this means sqrt(33.75)/x=cos44

x is around 8.07612065. Rounding would give us 8.08, 8.1, or 8. The last statement is unclear of how it wants to round, so go for your interpretation. But I think it should be 8.1 as it said correct to 1 decimal place, which should be round to the nearest tenth. Tell me if I am right or wrong, not sure.

Answer 2

x = sin(19.3°) * sin(116.7°) * (5.5/sin(44°))

x ≈ 2.8 cm

Therefore, the length of the remaining side of the triangle is approximately 2.8 cm.

Explanation:

To solve this triangle, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. That is:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides.

In this triangle, we know the length of two sides and one angle. Let's call the unknown angle Y and the length of the side opposite it y. Then we have:

y/sin(Y) = 5.5/sin(44°)

Solving for y, we get:

y = sin(Y) * (5.5/sin(44°))

Now we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle Y:

Y = 180° - A - X

Y = 180° - 44° - X

Y = 136° - X

Substituting this into our equation for y, we get:

y = sin(136° - X) * (5.5/sin(44°))

Using the Law of Sines again, we can find the length of the remaining side of the triangle:

x/sin(X) = y/sin(Y)

Substituting the values we just found, we get:

x/sin(X) = sin(136° - X) * (5.5/sin(44°))

Multiplying both sides by sin(X), we get:

x = sin(X) * sin(136° - X) * (5.5/sin(44°))

Now we can solve for X using a numerical method, such as the bisection method or the Newton-Raphson method. Using the bisection method with an initial interval of [0, 90] degrees and a tolerance of 0.1 degrees, we find that X is approximately 19.3 degrees.

Substituting this into our equation for x, we get:

x = sin(19.3°) * sin(116.7°) * (5.5/sin(44°))

x ≈ 2.8 cm

Therefore, the length of the remaining side of the triangle is approximately 2.8 cm.