babydrc2007
Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Question 4 of 5
Drag each label to the correct location on the triangle. Not all labels will be used.
Find the unknown measurements. Round all values to the nearest tenth.
cm
8.9 cm
65°

Question 4 Of 5 Drag Each Label To The Correct Location On The Triangle Not All Labels Will Be Used Find The Unknown Measurements Round All Values To The Neares class=

Sagot :

sqdancefan

Answer:

  • long side: 19.1 cm
  • missing angle: 25°
  • hypotenuse: 21.1 cm

Step-by-step explanation:

You can use this information to "guess" at the answers without doing any "work."

  • The sum of angles in a triangle is 180°.
  • The shortest side is opposite the smallest angle.

__

qualitative solution

The missing angle is the complement of the marked acute angle in the right triangle, so is ...

  C = 90° -65° = 25°

This angle is opposite the side of length 8.9 cm. The next-smallest angle is 65°, which is more than double the smallest angle. Hence the side opposite 65° will not be either of 3.8 or 9.8.

Of the two remaining measures, the longer one, 21.1, will be the hypotenuse, BC. The shorter of those, 19.1, will be the long side, AC.

Our solution is ...

  • AC = 19.1 cm
  • C = 25°
  • BC = 21.1 cm

__

quantitative solution

The mnemonic SOH CAH TOA reminds you of the relations between trig functions and right triangle sides. Here, we're given an angle and the length of its adjacent side. We are asked for the opposite side and for the hypotenuse. This suggests useful relations might be ...

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

Solving the first of these for the hypotenuse gives ...

  hypotenuse = adjacent/cos(65°)

  BC = 8.9 cm/cos(65°) ≈ 21.059 cm ≈ 21.1 cm

Solving the second relation above for the opposite side gives ...

  opposite = adjacent×tan(65°)

  AC = 8.9 cm×tan(65°) ≈ 19.086 cm ≈ 19.1 cm

As above, the missing angle is the complement of the given one:

  C = 90° -65° = 25°

Then the quantitative solution is ...

  • AC = 19.1 cm
  • C = 25°
  • BC = 21.1 cm

_____

Additional comment

If AC were 9.8 cm, the angle at B would be about 48°. That is, the two acute angles in the triangle would be very nearly equal.

We know that the side ratios in a 30°-60°-90° right triangle are 1 : √3 : 2. This triangle has a larger angle greater than 60°, so its longer side will be more than √3 times the short side. That means a length of 9.8 cm is way too short.

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.