Domanda del libro di testo
Find the area of the sector of a circle of radius r formed by a central angle θ. Express area in terms of π. Then round your answer to two decimal places. Radius, r: 4 inches Central Angle, θ: θ = 240°
638
views
Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
Capitolo 1, Problema 53
In Exercises 49–54, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.
Guida verificata passo dopo passo1
Identify the sides of the right triangle relative to the given angle of 39°. Here, side QR (51 m) is opposite angle P, and side RP is adjacent to angle P.
Determine which side length you need to find. For example, if you want to find side QP (the hypotenuse), use the sine or cosine function based on the given angle and known side.
Set up the trigonometric ratio using the angle and known side. For example, if finding the hypotenuse QP, use the cosine function: \(\cos(39^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{51}{QP}\).
Rearrange the equation to solve for the unknown side. For the hypotenuse, multiply both sides by QP and then divide both sides by \(\cos(39^\circ)\) to isolate QP: \(QP = \frac{51}{\cos(39^\circ)}\).
Calculate the value using a calculator (make sure it is in degree mode), then round the answer to the nearest whole number as required.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Right Triangle Properties
A right triangle has one angle of 90 degrees, and the other two angles sum to 90 degrees. The sides are related through trigonometric ratios, and the side opposite the right angle is the hypotenuse, the longest side.
Video consigliato:
Percorso guidato
5:35
30-60-90 Triangles
Trigonometric Ratios (Sine, Cosine, Tangent)
Sine, cosine, and tangent relate the angles of a right triangle to the ratios of its sides. For an angle θ, sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent. These ratios help find unknown side lengths.
Video consigliato:
Percorso guidato
5:08Sine, Cosine, & Tangent of 30°, 45°, & 60°
Using Given Angle and Side to Find Unknown Sides
Given one angle (other than 90°) and one side length, you can use trigonometric ratios to find the lengths of the other sides. Identify which side corresponds to opposite, adjacent, or hypotenuse relative to the given angle to apply the correct ratio.
Video consigliato:
Percorso guidato
4:18Finding Missing Side Lengths
Pratica correlata
Domanda del libro di testo
In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
-7𝜋/4
590
views
Domanda del libro di testo
Use reference angles to find the exact value of each expression. Do not use a calculator. sec 495°
676
views
Domanda del libro di testo
Express each angular speed in radians per second. 6 revolutions per second
673
views
Domanda del libro di testo
In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
16𝜋/3
614
views
Domanda del libro di testo
In Exercises 49–54, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.
<Image>
543
views