Noah and Brianna want to calculate the distance between their houses which are opposite sides of a water park. They mark a point A, 120m long the edge of the water park from Briannas house. The meansure <NBA as 75degree and <BAN as 70 degree. Determine the distance between their houses.
Really don't understand need help.please
To determine the distance between Noah and Brianna's houses, we can use the Law of Sines. Let's break down the problem and find a solution step by step.
Step 1: Draw a diagram
Start by drawing a diagram to visualize the situation. Draw three points: Noah's house (N), Brianna's house (B), and the marked point (A) along the edge of the water park.
Step 2: Label the diagram
Label the distance between Noah's house and the marked point as "x."
Step 3: Use the information given
From the information given in the problem:
- The measure of angle NBA is 75 degrees.
- The measure of angle BAN is 70 degrees.
- The distance from Brianna's house to the marked point is 120m.
Step 4: Apply the Law of Sines
The Law of Sines states that for any triangle, the ratio between the length of a side and the sine of the opposite angle is constant. In equation form, it is represented as:
a/sin(A) = b/sin(B) = c/sin(C)
In our case, we can use this law to find the length of side x. The relevant parts of the equation are:
a = 120m (side opposite angle BAN)
A = 75 degrees (angle opposite side x)
B = 70 degrees (angle opposite side 120m)
Therefore, we have:
x/sin(75) = 120/sin(70)
Step 5: Solve the equation
To find the value of x, we can rearrange the equation and solve for x using basic algebra:
x = (120m * sin(75)) / sin(70)
Using a scientific calculator, we can evaluate the right side of the equation and find the value of x.
Step 6: Calculate the value of x
Using the given values, evaluate the expression:
x = (120m * sin(75)) / sin(70)
After calculating this expression, you will find the value of x, which represents the distance between Noah and Brianna's houses.