Question

Tiffany, Lori, and Mika are practicing for an egg-tossing contest. The distance from Tiffany to Lori is 17 inches. The distance from Lori to Mika is 32 inches. The distance from Mika to Tiffany is 28 inches. Find the measures of the three angles in the triangle.

Answer 1

Measure of 3 angle in triangle is : 32 degree,  61 degree  and 87 degree

Answer 2

Answer:

$87^{\circ},61^{\circ}\text{ and }32^{\circ}$.

Step-by-step explanation:

Please find the attachment.

We have been given that the distance from Tiffany to Lori is 17 inches. The distance from Lori to Mika is 32 inches. The distance from Mika to Tiffany is 28 inches.

Upon looking at our attachment, we can see that Tiffany, Lori and Mika form a triangle. We will use Law of cosines to solve for measure of each angle.

$c^2=a^2+b^2-2ab\cdot \text{cos}(C)$, where, a, b and c are sides opposite to angles A, B and C respectively.

Upon substituting our given values in law of cosines, we will get:

$17^2=32^2+28^2-2(32)(28)\cdot \text{cos}(C)$

$289=1024+784-1792\cdot \text{cos}(C)$

$289=1808-1792\cdot \text{cos}(C)$

$-1519=-1792\cdot \text{cos}(C)$

$-1792\cdot \text{cos}(C)=-1519$

$\frac{-1792\cdot \text{cos}(C)}{-1792}=\frac{-1519}{-1792}$

$\text{cos}(C)=0.84765625$

Now, we will inverse cosine (arccos) to solve for angle C.

$C=\text{cos}^{-1}(0.84765625)$

$C=32.042342044071^{\circ}$

$C\approx 32^{\circ}$

Similarly, we will find measure of angle A.

$a^2=b^2+c^2-2bc\cdot \text{cos}(A)$

$32^2=28^2+17^2-2(28)(17)\cdot \text{cos}(A)$

$1024=784+289-952\cdot \text{cos}(A)$

$1024=1073-952\cdot \text{cos}(A)$

$-49=-952\cdot \text{cos}(A)$

$-952\cdot \text{cos}(A)=-49$

$\frac{-952\cdot \text{cos}(A)}{-952}=\frac{-49}{-952}$

$\text{cos}(A)=0.0514705882352941$

$A=\text{cos}^{-1}(0.0514705882352941)$

$A=87.049648856989^{\circ}$

$A\approx 87^{\circ}$

Now, we will use angle sum property to solve for angle B as:

$m\angle A+m\angle B+m\angle C=180^{\circ}$

$87^{\circ}+m\angle B+32^{\circ}=180^{\circ}$

$m\angle B+119^{\circ}=180^{\circ}$

$m\angle B+119^{\circ}-119^{\circ}=180^{\circ}-119^{\circ}$

$m\angle B=61^{\circ}$

Therefore, the angles of our triangle would be 87 degrees, 61 degrees and 32 degrees.