In which triangle is the measure of the unknown angle, x, equal to the value of sin–1(StartFraction 5 Over 8. 3 EndFraction)?.
1 answer:
The triangle is a right-angled triangle with a perpendicular side of 5 and a hypotenuse of 8.3.
<h2 /><h2>Given to us</h2>as we know that sine for any angle is the ratio of its perpendicular to the hypotenuse, and trigonometry is only applicable to a right-angled triangle.
therefore,
Hence, the triangle is a right-angled triangle with a perpendicular side of 5 and a hypotenuse of 8.3.
Learn more about Sine:
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Answer:
#5: 180 paperclips in total.
#6: 126 stamps in total.
#7: Elena should give Lucy 15 colored pencils.
Step-by-step explanation:
This explanation solves each question by setting a single unknown, .
Let the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.
Initially:
- Antonio:
paperclips;
- Abby:
Antonio gives paperclips to Abby. After that,
- Antonio:
paperclips;
- Abby:
paperclips.
Abby now possess twice as many paperclips as Antonio does. In other words,
.
By the distributive property:
.
Substract from both sides
.
Both Antonio and Abby initially possess 90 paperclips. That's 180 in total.
<h3>#6</h3>Similarly, let be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.
Initially:
- Emily:
- Jasmine:
After Emily gives stamps to Jasmine:
- Emily:
stamps;
- Jasmine:
stamps.
Jasmine now possesses twice as many stamps as Emily does. In other words,
.
.
Jasmine used to possess 126 stamps. Now she possesses stamps after receiving
stamps from Emily.
Let the number of pencils that Elena needs to give to Lucy be .
Initially:
- Elena: 60 pencils;
- Lucy: 26 pencils.
After Elena gives pencils to Lucy:
- Elena:
pencils;
- Lucy:
pencils.
Elena should now possess four more pencils than Lucy does. In other words,
.
.
.