Solve the right triangle ABC with right angle C if B=30 degrees and c=10.

2 answers:

4 0

aâ‰8.6602, b=5, A=60 degrees Let's calculate the lengths of the sides and angles and see what option fits. Since the sum of the angles in a triangle equals 180 and we known 2 of the angles, let's calculate angle A first. A = 180 - 90 - 30 = 60 Now for side b. This is a 30/60/90 triangle. The side opposite B is half the length of c since if you were to reflect the triangle across side a, you would have an equilateral triangle. So b is 10/2 = 5. And finally, since we have a right triangle, we can use the Pythagorean theorem to get the remaining side a. So a = sqrt(10^2 - 5^2) = sqrt(100 - 25) = sqrt(75) = 5*sqrt(3) â‰ 8.660254038 And of the available choices, only the last one matches which is aâ‰8.6602, b=5, A=60 degrees As a side note, the last option comes close, but isn't entirely correct since the properly rounded value for a should be 8.6603, not 8.6602.

kenny6666 [7]3 years ago

3 0

C=10, C=90°, B=30°, A+B+C=180°
A+30°+90°=180°⇒A=60°

cos30°=a/c
cos30°=a/10⇒a=cos30°*10
a≃8.6602

c²=a²+b²⇒b²=c²-a²
b²=10²-8.6602²⇒b²=25
b=5

You might be interested in

Can you answer this?

nignag [31]

The answer is the graph b.

4 0

2 years ago

Which biconditional is not a good definition?

Xelga [282]

The correct answers are:

A ray is a bisector of an angle if and only if it splits the angle into two angles; and
A) I can afford to buy a ticket.

Explanation:

For the first question, the first three answers are very specific and true:

A whole number is odd if it is not divisible by 2, and a number is not divisible by 2 if it is odd;
an angle is straight if its measure is 180 degrees, and the measure of an angle is 180 degrees if it is a straight angle;
a whole number is even if it is divisible by 2, and a number is divisible by 2 if it is even.

However, with the fourth choice, we are missing a key word in the definition. A ray is a bisector of an angle if and only if it splits the angle into two CONGRUENT angles. It is not just a ray that cuts an angle into two pieces, the pieces must be equal.

For the second question, the Law of Detachment says if our conditional "if p, then q" is true and p is true, then q must also be true.

For this question, "I can go to the concert if I can afford to buy a ticket" is true as well as "I can go to the concert." This means "I can afford to buy a ticket" must be true as well.

4 0

3 years ago

You place the spring vertically with one end on the floor. You then drop a book of mass 1.50 kg onto it from a height of 0.900 m

Alex777 [14]

Answer:

The value of the maximum distance the spring will be compressed

x = 0.143 m= 14.3 cm

Step-by-step explanation:

Given data

Mass m = 1.5 kg

h = 0.9 m

k = 1500 $\frac{N}{m}$